An effective method to analyze the origin of primary dark counts is presented for single-photon-detection avalanche photodiodes (APDs) operated in the gated Geiger modes. It is revealed that a band-to-band tunneling model reproduces the experimental data very well for GaInAs/InP single-photon-detection APDs, while a phonon-assisted tunneling model fails. Therefore, we concluded that primary dark counts are dominated by the band-to-band tunneling for the GaInAs/InP single-photon-detection APDs. Then, we calculate the dark count probability and the detection efficiency by modeling the band-to-band tunneling. It is found that the ratio of the dark count probability to the detection efficiency is reduced by decreasing the impurity concentration of the multiplication region and of the p-type window.