As a method beyond the mean-field analysis, a matrix product state (MPS) with incommensurate periodicity is applied to detection of phase transitions accompanied with periodicity change. The incommensurate MPS is constructed by acting local-spin-rotation operators with the incommensurate periodicity on a uniform MPS. As a commensurate/commensurate change, we calculate the partial ferro -perfect ferro phase transition in the S = 1/2 Heisenberg model and its critical exponent of the magnetization curve. As a commensurate/incommensurate change, we calculate the S = 1 Heisenberg model with bilinear and biquadratic interactions which has periodicity change in the spin-spin correlation function.