Direct cell-to-cell transfer of HIV-1 is found to be a more potent and efficient means of virus propagation than virus-to-cell infection. In this paper we propose a mathematical model to consider these two modes of viral infection and spread, in which infection age is also incorporated. By a rigorous analysis of the model, we show that the model demonstrates a global threshold dynamics, fully described by the basic reproduction number, which is identified explicitly. The formula for the basic reproduction number of our model reveals that the basic reproduction number of a model that neglects either cell-to-cell spread or virus-to-cell infection might be underevaluated.