We perform a 3D-MHD simulation of a self-gravitating isothermal gas layer that is initially penetrated by a uniform magnetic field. The strength of the initial magnetic field is such that the cloud is slightly subcritical. In this system, we input random supersonic turbulence initially. Ion-neutral friction is also introduced in the magnetized gas so that the magnetic diffusion allows gas to go across the magnetic field and form self-gravitating cores. We found that self-gravitating cores are formed in the dense region enhanced by the shock waves if ion-neutral friction is introduced. The time scale of core formation is on the order of the 106 years, which is faster than the usual magnetic diffusion time (107 years) estimated from the initial condition. Our result is consistent with the results of 2D-MHD simulations by Li & Nakamura (2004).