  We propose a new variational Monte Carlo (VMC) approach based on the Krylov
subspace for large-scale shell-model calculations. A random walker in the VMC
is formulated with the $M$-scheme representation, and samples a small number of
configurations from a whole Hilbert space stochastically. This VMC framework is
demonstrated in the shell-model calculations of $^{48}$Cr and $^{60}$Zn, and we
discuss its relation to a small number of Lanczos iterations. By utilizing the
wave function obtained by the conventional particle-hole-excitation truncation
as an initial state, this VMC approach provides us with a sequence of
systematically improved results.
