Recently a pseudogap with d-wave symmetry was observed near the Fermi level in photoemission spectra of normal-state Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8} crystals. We demonstrate that an analogous pseudogap exists in the energy spectrum of the two-dimensional t-J model of cuprate perovskites. In agreement with experiment the magnitude of the pseudogap is 10{endash}20 meV in underdoped crystals with hole concentration x{approx_lt}0.17 and the pseudogap disappears in optimally and overdoped crystals when x{approx_gt}0.17. We demonstrate also that in the t-J model the overall energy spectrum near the Fermi level and the Fermi surface agree well with experimental observations. {copyright} {ital 1997} {ital The American Physical Society}