We constructed a countable space of p-adic periods for 1- motives with good reduction using the crystalline-de Rham comparison isomorphism and formulated a p-adic period conjecture analogous to clas- sical periods. To establish these periods, it is necessary to identify a ”suit- able” Betti-like Q-structure inside the crystalline realization. We demon- strated that these p-adic numbers arise from our developed p-adic integra- tion theory for 1-motives with good reduction, generalized from the classical Fontaine-Messing p-adic integration theory. Furthermore, we proved the so- called p-adic subgroup theorem for 1-motives, which implies the validity of the p-adic period conjecture for these 1-motives. Consequently, this implies that a p-adic version of the Kontsevich-Zagier period conjecture holds for smooth curves with good reduction.