Although born on the east coast, Henry Rankin Poore was raised in California. Moving to New York in 1876, he studied for a year in the NAD Antique School. Several years later, he was in Philadelphia, taking classes at the Pennsylvania Academy of Fine Arts under Peter Moran. With Moran, Poore traveled to New Mexico in 1882 in order to study the Pueblo Indians for the U.S. government. He made a similar trip West at the end of the decade.
After graduating from the University of Pennsylvania in 1883, Poore left for two and a half years in Europe, where his teachers included William-Adolphe Bouguereau. While in England, he became enamored of fox hunting; the depiction of hunting dogs became a standard subject for him. Poore returned to Philadelphia but sent works regularly to New York for the NAD Annuals. In 1888 he won the Academy's Second Hallgarten Prize, no doubt prompting his election as an Associate.
A second European trip took Poore to France and England in the early 1890s. He was called home, however, to become professor of composition at the Pennsylvania Academy of Fine Arts. His 1896 marriage to Katherine Stevens resulted in a move to Orange, New Jersey, which became his permanent residence for the rest of his life. Around the turn of the century, however, Poore discovered the art colony at Old Lyme, Connecticut. He began to spend his summers there and developed a new subject, hazy, soft landscapes without animals. At this time, he also began publishing a series of books expressing his conservative views on art theory and criticism. He continued to submit works to Academy Annuals until close to his death.