Summary: We consider the branching process \(Z_n =X_{n, 1} + \dots +X_{nZ_{n-1}} \) in random environments \(\boldsymbol{ \eta}\), where \(\boldsymbol{ \eta}\) is a sequence of independent identically distributed variables and for fixed \(\boldsymbol{ \eta}\) the random variables \(X_{i, j}\) are independent, have the geometric distribution. We suppose that the associated random walk \(S_n = \xi_1 + \dots + \xi_n\) has positive mean \(\mu\) and satisfies the right-hand Cramer’s condition \(\mathbf{E}\) \(\exp (h \xi_i ) < \infty\) for \(0<h<h^+\) and some \(h^+\). Under these assumptions, we find the asymptotic representation for local probabilities \(\mathbf{P}(Z_n =\lfloor \exp(\theta n) \rfloor )\) for \(\theta \in [ \theta_1, \theta_2] \subset ( \mu;\mu^+)\) and some \(\mu^+\).