The Susceptible-Infected-Removed (SIR) model's epidemic dynamics on complex networks with immunizations were studied, and the effects of immunizations on the spread of epidemic were discussed. When vaccinal ratio is greater than zero, the critical infection value becomes greater with the time increasing. Therefore vaccination can indeed prevent and control the spreading of diseases on complex networks. In further details, this paper discussed the epidemic threshold for disease spreading using SIR model with piecewise linear infectivity on scale-free networks. And with this nonlinear infectivity,the conditions for positive epidemic threshold were derived. Then various immunization strategies for the SIR model and the corresponding thresholds were discussed. Numerical simulations and comparisons show that the targeted immunization is more effective than random immunization, acquaintance immunization and active immunization strategies.