We develop a pricing model for convertible bonds with dividend protection subject to credit risk by extending the models developed by Tsiveriotis and Fernandes (TF), and by Ayache, Forsyth and Vetzal (AFV). We consider two techniques to incorporate the dividend protection feature: Conversion Ratio Adjustment and Dividend Pass-Thru. We apply finite difference methods to discretize the PDEs associated with our models, and study the Projected Successive Over-Relaxation and penalty methods to handle the free boundaries. We compare these two methods in terms of convergence rate, number of iterations per time step and computation time for pricing convertible bonds without dividends. Finally we apply the penalty method, the better of the two methods, to solve the systems arising from our models for convertible bonds with dividend protection. We examine the convergence rates and discuss the difference between the results from the extended TF and AFV models, with both dividend protection techniques.