The dynamics of epidemic spreading on time evolution network has attracted much attention. Here we present an alternate network, changing between scale free network and one-to-one random network, to simulate the topology structure between day and night. In our work, introducing the concept of effective contact, we investigate the epidemic spreading of SIR (susceptible-infected-recovered) model on the alternate network. Remarkably and quite excitingly, we find that spreading velocity is smaller on the alternate network than on scale free network. Numerical studies show that most of infected individuals do not keep disease state longer and will go to recovery state after a short time. We also study the recovery number as a function of the transmission rate and recovery probability.