Browning still projects strong image; Robert Browning: A Life Within Life, by Donald Thomas. New York: The Viking Press. 334 pp. $20.95.

Here is a fine new biography of a great writer who seems to be out of favor with contemporary readers. That's surprising, because the influence of the dramatic monologue as perfected by Browning can be seen in T. S. Eliot, Robert Frost, and dozens of their followers and imitators - and because there's ample evidence of the powerful image Browning has long projected.

Thomas's book operates on the long-held inference that Browning hid his real thoughts and feelings behind a ''defensive wall of privacy'' and led a carefully concealed ''life within life.'' Its method, therefore, is to present a close analysis of Browning's enormous poetical output in order to demonstrate how his busy, combative, and complicated thought-process worked.

It was an intellect formed under the loving, indulgent influence of parents who fed his hunger for learning and desire to become a poet. Just as their own avocations stimulated young Robert's interest in music and art, so did their liberal (nonconformist) religious faith bequeath him an invigorating compound of idealism and skepticism - which, perhaps, produced that ''optimism and robustness'' that kept him working steadily through the years when his poems were ignored or savaged by most of his contemporaries.

For Browning's notorious ''morbidity,'' his interest in the criminal and psychopathic minds, and his probing studies of aggressive emotions scarcely pleased the public that had made a hero and poet laureate, as it happened, of his lifelong rival, Tennyson. Early in his career he had displayed a posturing ''atheism . . . acquired from Shelley''; add to this his increasingly well-known moodiness and pugnacity - and there resulted a public perception that Browning was something less than a gentleman, and considerably less than a major poet.

Thomas skillfully traces the continuance of such frustrations throughout Browning's long life (1812-89). His early years, spent writing verse dramas, caused ''much of his early genius and energy . . . to be lost.'' His storied marriage to Elizabeth Barrett - whose poetic fame far exceeded his - surely focused and elevated Browning's sympathetic emotions, yet the defensive tactics by which he made himself live through the sorrow of her early death may have hardened him into attitudes that helped drive potential readers, and comprehenders, still further away.

There's no shrinking here from a frank portrayal of ''Browning in the years of his triumph,'' absurdly oversensitive and vindictive, known for the ''noisy and comic vanity'' he showed to influential people who now wined and dined him, and lionized him. Thomas makes us understand that when ''the honours and rewards , withheld for so many years, came to him at last,'' Browning could not keep from luxuriating in the attention he knew he had always merited.

Thomas adroitly shows us how the complexity of Browning's personality shows through strongly in his rich and varied oeuvre. The abrasive Shelleyian romantic is on display in the fulsome and tedious ''Pauline'' (1832), a disaster that nearly destroyed his reputation for all time. The love of learning, which sometimes deadened his work, appeared to brilliant advantage in the estimable long poem ''Paracelsus'' (1835). The erotic intensity that was surely dominant in his own nature enlivened the many lyrics and monologues gathered in such landmark collections as ''Men and Women'' and ''Dramatis Personae.'' And his interest in morbid pyschology reached an unforgettable zenith in his verse novel based on an aristrocratic Roman family's domestic tragedy, ''The Ring and the Book'' (1869).

As I read on, I was more and more impressed to realize how much of Browning's poetry has remained on the edge of my memory, and still seems, now that I'm reminded of it, as vividly original as ever. Browning's admirers, therefore, as well as those just beginning to read him, should find this incisive biography a perfect introduction to his work.