  We consider the branching random walks in $d$-dimensional integer lattice
with time--space i.i.d. offspring distributions. Then the normalization of the
total population is a nonnegative martingale and it almost surely converges to
a certain random variable. When $d\geq3$ and the fluctuation of environment
satisfies a certain uniform square integrability then it is nondegenerate and
we prove a central limit theorem for the density of the population in terms of
almost sure convergence.
