In previous modelling efforts to understand the spreading process on networks, each node can infect its neighbors and cure spontaneously, and the curing is traditionally assumed to occur uniformly over time. This traditional curing is not optimal in terms of the trade-off between the effectiveness and cost. A pulse immunization/curing strategy is more efficient and broadly applied to suppress the spreading process. We analyze the pulse curing strategy on networks with the Susceptible-Infected (SI) process. We analytically compute the mean-field epidemic threshold $\tau_c^{p}$ of the pulse SI model and show that $\tau_c^{p}=\frac{1}{\lambda_1}\ln\frac{1}{1-p}$ , where $\lambda_1$ and p are the largest eigenvalue of the adjacency matrix of the contact graph and the fraction of nodes covered by each curing, respectively. These analytical results agree with simulations. Compared to the asynchronous curing process in the extensively studied Markovian SIS process, we show that the pulse curing strategy saves about 36.8%, i.e., $p\approx 0.632$ , of the number of curing operations invariant to the network structure. Our results may help policymakers to design optimal containment strategies and minimize the controlling cost.