We propose a new method to design novel structure of phase-shifted long period grating by adding a modulated structure in a long period grating somewhere, which performs an accumulated phase shift. Based on the phase-match theory, the relation between the phase shift and parameters of the grating is derived, while the modulated structure is a uniform short grating and its modulated depth remains the same. This new theory is simulated with the transmission matrix method and the validity is proved by experimental fabrication with CO2 laser. The study shows that adding a uniform short grating in a long period grating can form a phase-shift long period grating. And the spectrum only depends on the length of modulated sturcture, in the case that its modulated depth of refractive index is the same as the original one.