In this paper, a new grating-diffraction interferometry with partially coherent illumination is proposed. As a foundation, the partially coherent diffraction effect of gratings between the Talbot and the Lau effects is firstly treated. A new type of interferogram is resulted in such a new interferometer, that is characterized by two gratinglike carriers of doubled spatial frequency. Simply by the adjust-ment of the source slit the interferometer will become the Talbot interferometer and the Lan interferometer, respectively, at the two extremes of illuminatoin coherence. The performance of the system is analysed by the ambiguity function. Experiments are given too.