In this paper, we perform a theoretical study of the all-optical logic gates based on the techniques of cross phase modulation (XPM) in a phase-shifted grating. Here the pumps are used to control the switching of a weak continuous wave (cw). In order to understand the transferring process of the information from the pump light to the cw light, we first study the switching characteristic of the device. Then, by changing the combination between two pumps, in a fiber grating with zero phase shift we have realized NOT, AND, and NAND gates, and in a phase-shifted grating with the phase shift π, the other various logic operations can be realized such as NAND gates and OR gates; when selecting Δφ=3/2π, we can realize XOR gates and XNOR gates. Thus the change of the phase shift of the phase-shifted grating will yield various logic gates.