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In this paper, we derive the Laguerre operational matrix (LOM) of fractional derivatives, which is applied together with the spectral tau method for numerical solution of general linear multi-term fractional differential equations (FDEs) on the half line. A new approach implementing Laguerre operational matrix in combination with the Laguerre collocation technique is introduced for solving nonlinear multi-term FDEs. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations, greatly simplifying the problem. The proposed methods are applied for solving linear and nonlinear multi-term FDEs, subject to initial conditions, and the exact solutions are obtained for some tested problems. doi:10.14456/WJST.2014.59