This article proposes a new numerical approach for solving fractional optimal control problems including state and control inequality constraints using new biorthogonal multiwavelets. The properties of biorthogonal multiwavelets are first given. The Riemann-Liouville fractional integral operator for biorthogonal multiwavelets is utilized to reduce the solution of optimal control problems to a nonlinear programming one, to which existing, well-developed algorithms may be applied. In order to save the memory requirement and computation time, a threshold procedure is applied to obtain algebraic equations. The method is computationally very attractive and gives very accurate results.