Motivation. 2D Ising model with competing interactions describes the thermodynamic properties of confined complex liquids like microemulsion films and some compounds of rare-earth metals. On the other hand there is a close relationship between critical properties of this model and peculiarities of the energy spectra of some onedimensional quantum models Therefore correct description of model phase diagram is of wide interest. Method. Density matrix renormalization group method for two-dimensional classical systems. Results. A new modification of density matrix renormalization scheme for 2D Ising model with competing interactions has been presented. The estimations for critical temperatures of second order phase transitions in the model were obtained. Conclusions. 2D Ising model with competing interactions has a complicated phase diagram and can be described by means of corresponding version of DMRG method at least in the vicinity of some critical points.