Collisions of monodispersed particles in turbulent flows are important both in the mechanical engineering and in the cloud microphysics. A number of studies investigated the phenomenon but they neglected the gravity acting on the particles in order to assume the isotropy of particle motions. In this study, therefore, we investigated the effect of the gravity on the collision frequency by using a direct numerical simulation. The results show that if we neglect the particle weight, i.e. the gravity, is neglected the collision frequency becomes higher. It is also found that when the particle terminal velocity is comparable to or greater than the root mean square value of the fluid velocity the particle weight cannot be neglected.