A study on the lithium abundance in 36 T Tauri stars (mass range 0.4-2.25 solar masses), partly based on high-dispersion spectra taken with the Isaac Newton Telescope, is presented. A study of non-LTE effects in the formation of the lithium double in T Tauri stars and derived corrections to the abundances in the LTE in the range 1.0-4.0 log N(Li) is presented. Tor T(eff) of 400-4500 K, a significant upward correction to the LTE abundance (about 0.3-0.6 dex) is found. For T(eff) close to 500 K, smaller corrections (about 0.2 dex), and for log N(Li) greater than about 3, downward corrections (about 0.1 dex) are found. The initial value of the lithium abundance in T Tauri stars is estimated at 3.2 +/- 0.1, which is in close agreement with the accepted present cosmic abundance.