In this paper, we investigate the dynamical behavior of a nonlinear model for viral infection with humoral immune response and two discrete delays. The model is a four-dimensional system which describes the interactions of the virus, uninfected target cells, infected cells and B cells. We assume that the incidence rate and removal rate of infected cells are given by general nonlinear functions. We derive two threshold parameters, the basic reproduction number \(R_{0}\) and the humoral immunity number \(R_{1}\). Utilizing Lyapunov functionals and LaSalle’s invariance principle, the global asymptotic stability of the steady states of the model has been studied. We have established a set of sufficient conditions which guarantee the global stability of the model. We have proven that (1) if \(R_{0}\le 1\), then the infection-free steady state is globally asymptotically stable (GAS), (2) if \(R_{1}\le 1 1\), then the chronic-infection steady state with humoral immune response is GAS. We introduce an example and conduct some numerical simulations to confirm our theoretical results.