This paper presents an efficient numerical method to solve fractional infinite-horizon optimal control problems, where the dynamic control system depends on Caputo fractional derivatives. First, by a suitable change of variable, we transform the fractional infinite-horizon optimal control problem to a finite-horizon one. Then, with the help of an approximation, we replace the Caputo derivative to integer order derivative. According to the Pontryagin minimum principle (PMP) for optimal control problems and by constructing an error function, we define an unconstrained minimization problem. In the optimization problem, we use trial solutions for state, costate and control functions where these trial solutions are constructed by using two-layered perceptron neural network. Some numerical results are introduced to explain our main results.