  We study eigenvalue distribution of the adjacency matrix $A^{(N,p, \alpha)}$
of weighted random bipartite graphs $\Gamma= \Gamma_{N,p}$. We assume that the
graphs have $N$ vertices, the ratio of parts is $\frac{\alpha}{1-\alpha}$ and
the average number of edges attached to one vertex is $\alpha\cdot p$ or
$(1-\alpha)\cdot p$. To each edge of the graph $e_{ij}$ we assign a weight
given by a random variable $a_{ij}$ with all moments finite.
  We consider the moments of normalized eigenvalue counting measure
$\sigma_{N,p, \alpha}$ of $A^{(N,p, \alpha)}$. The weak convergence in
probability of normalized eigenvalue counting measures is proved.
