This paper investigates the non-overshooting tracking problem as to a class of fractional order linear time invariant (FO-LTI) and multi-input multi-output (MIMO) systems. A method is provided for designing the state feedback controller to asymptotically track the step references without non-overshooting. The state feedback matrix F proposed here can take from the combined eigenvalue and eigenvector placement methods given in Moore. The state feedback matrix F can control the system's overshooting. The decay rate of non-overshooting controller can be arbitrary and only be determined by the expected eigenvalues. Finally, a numerical example illustrates the effectiveness of the proposed method.