A new weighted network model with accelerating growth was presented. Companed with the previous models where weights are assigned statically or rearranged locally, this model allows the flows to be widely updated, and gives powerlaw distributions of degree, weight and strength, respectively. Particularly, the exponents are nonuniversal and depend on two network parameters. It turns out that the strength highly correlates with the degree and displays scalefree property, which is consistent with empirical evidence. Simulations were provided to demonstrate the theoretical results.