Abstract: The first experimantal realization of Bose-Einstein consensate in 1995 attracted a lot attention to these problems. The subsequent development of technical instruments brought, in particular, a progress in manipulating ultracold particles by optical methods. A large part of Bose gas experiments is at present realized using so-called optical lattices. It is an instrument to capture and control bosons which allows us to observe interesting effects. In the first part we will present and discuss a model describing a Bose gas in a one-dimensional optical lattice. The next part is devoted to description of the Density Matric Renormalization Group algorithm (DMRG) which can be used in an elegant way just to analyse one-dimensional systems. Finally the algorithm will be applied to derive information about properties of the above mentioned model.