In this paper, in order to search the reason of the phenomena of power- law in the weighted networks, we present a general model for the growth of weighted networks that couples of new edges and vertices and the weights’ and intrinsic strengths’ dynamical evolution. This model is based on a simple weight and intrinsic strength driven dynamics and generates networks exhibiting the statistical properties observed in several real-world systems. Within this model we not only yields the scale-free behavior for the weight, strength and degree distributions, but also we give the analytical computation of the distributions of the weight, the strength and the degree .Simultaneity, by way of contrasting our results with those of the random model, we found the preferential attachment is necessary to the phenomena of scale-free of the strength and degree distributions. Finally, we found the analytical results are good consistent with those of numerical simulation. The conclusion from this model is helpful to the investigation of the topological role of weight and strength.