It is shown that d-symmetry superconductivity due to valence bond correlations is possible. Valence bond correlations are compatible with antiferromagnetic spin order. In order to explictly construct a homogeneous state with the valence bond structure in the two-dimensional Hubbard model for an arbitrary doping, we have used the variational method based on unitary local transformation. Attraction between holes in the d-channel is due to modulation of hopping by the site population in course of the valence bond formation, and corresponding parameters have been calculated variationally. An important factor for the gap width is the increase in the density of states on the Fermi level due to antiferromagnetic splitting of the band. The gap width and its ratio to the T_c are 2Δ approx= 0.1 t and 2Δ/kT_c approx= 4.5 - 4 for U/t approx= 8. The correspondence between the theoretical phase diagram and experimental data is discussed. The dependence of T_c on the doping δ = |n - 1| and the Fermi surface shape are highly sensitive to the weak interaction t' leading to diagonal hoppings. In the case of t' > 0 and p-doping, the peak on the curve of T_c(δ) occurs at the doping δ_(opt), when the energy of the flattest part of the lower Hubbard subband crosses the Fermi level at k ～ (π,0). In underdoped samples with δ < δ_(opt), the anisotropic pseudogap in the normal state corresponds to the energy difference |E(π,0) - μ| between this part of the spectrum and the Fermi level.
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