  We investigate the phase diagram of two-dimensional (2D) Hubbard model by
employing the optimization variational Monte Carlo method. The 2D Hubbard model
is the most simple electronic model for cuprate high-temperature
superconductors. The phase diagram consists of three regions; they are
antiferromagnetic insulator (AFI) region, superconducting (SC) region and the
coexistent region of superconductivity and antiferromgantism. The phase diagram
obtained by numerical calculations well agrees with the experimental phase
diagram for high-temperature cuprates. We mainly focused on the effect of $t'$
on the antiferromagnetic (AF) correlation and the AFI region. The area of the
AF phase increases when we include $t'$ and thus the pure $d$-wave SC phase
decreases. The AFI phase near half filling decreases as $|t'|$ increases.
