In recent years the non-commutativity problem in the string theory has been controversial. In order to find non-commutativity one should first quantize the theory and find the algebra between fields. In this thesis we try to introduce and investigate the ordinary quatization methods and use them to quantize the “bosonic string in a non-flat background and time-dependent B field” that was provided by Nappi and Witten. First we introduce the action that are used in string theory. In Second chapter we introduce the symmplectic quantization method. Then by investigating the constraint structure we intent to provide mode expansion for original fields. In this procedure we explain important problems that one should observe in order to provide a suitable mode expansion. Then we try to find a mode expansion for Nappi-Witten model (bosonic string in a non-flat background and time-dependent B field) using lagrangian approach. This approach yields a time-dependent Poisson bracket. To give an alternative approach we investigate the constraint structure and symmetries of this model and by introducing two gauge fixing conditions we try to provide a suitable mode expansion.