In this paper, a Hadamard transform imaging spectrometer(HTIS) is proposed by using a grill spectrometer. And we reconfigure the system by using the grill sectrometer which uses a left cyclic S-matrix instead of the conventional right cyclic one. Then, we model the Hadamard transform imaging spectrometer and apply the mask characteristics compensation method, i.e. $ {T}^{-1}$ method, to complete fast algorithm. Also, through computer simulations the superiority of the proposed system in this paper to the conventional Hadamard transform spectrometer(HTS) is proved and the performance of the two systems are compared by introducing average mean square error(AMSE) as the algebraic criterion.