This study explored the feasibility of using the Radau pseudospectral method (RPM) to optimize the energy management strategy for a hybrid tracked vehicle. The engine–generator set and the battery pack of the serial hybrid tracked vehicle were modeled and validated through the bench test. A DC-DC converter was equipped between the battery pack and the DC bus in this hybrid powertrain, which increased the flexibility of energy distribution between the engine–generator set and the battery. It was simplified as a voltage regulator in the hybrid powertrain model. The power demand during the vehicle operation was calculated according to the vehicle dynamics and driving schedules. The optimal control problem was formulated to minimize the fuel consumption through regulating the power distribution properly between the engine–generator set and battery pack during a typical driving schedule. The RPM was applied to transform the optimal control problem to a finite-dimensional constrained nonlinear programming problem. A comparison of the solutions from RPM and dynamic programming showed that the former offers the higher computation efficiency and better fuel economy.