This paper investigate the mathematical properties of generalized policy iteration (GPI) applied to a class of continuous-time linear systems with unknown internal dynamics. GPI is a class of dynamic programming (DP) method to solve an optimal control problem by using two consecutive steps-policy evaluation and policy improvement. We first provide several formula equivalent to GPI, and as a result, reveal its relations to linear quadratic optimal control problems and the fact that the computational complexity due to backup operations in policy evaluation steps can be lessened by increasing the time horizon of GPI. A variety of local stability and convergence criteria is also provided with the connection to the convergence speed. Finally, several numerical simulations are performed to verify the results.