We propose and investigate a class of aperiodic grating structure which can achieve perfect Talbot effect under certain conditions. The aperiodic grating structure is obtained by the superposition of two or more sine terms. In the case of two sine terms, the Talbot effect can be realized when the period ratio of two terms is arbitrary. While in the case of more than two sine terms, the period ratios of each term must meet certain extra conditions. The theory has been further verified by numerical simulations. It expands the field of Talbot effect and is of potential significance for subsequent research applications such as optical imaging and measurement.