We perform a Hamiltonian analysis of the Green-Schwarz sigma model on a supercoset target with Z4m grading. The fundamental Poisson brackets between the spatial component of the flat currents depending on a continuous parameter, which can be thought of as a first step in the complete calculation of the algebra of the transition matrices, are obtained. When m = 1, our results are reduced to the results of the type IIB Green-Schwarz superstring on AdS5×S5 background obtained by Das, Melikyan and Sato.
