Based on the discrete form of the target-missile relative motion equations in plane, a discrete sliding-mode guidance (DSMG) law is proposed. All previous missile seeker's measurements are used in the design of the DSMG law to estimate the target acceleration such that noises in the seeker's measurements are effectively being smoothened. It is proved that the proposed DSMG law is finite time convergent. Quasi sliding-mode bands of the DSMG law are discussed, and the formula for calculating the terminal miss distances of the missile under the DSMG law are presented. Simulation results from a space interception process verify the effectiveness of the proposed method.