In this paper, a finite-time stabilized guidance law is addressed in presence of some measurement noises. The measurement noise would effect on the guidance system stability and or performances. Hence, in presence of measurement noise, the guidance law must be modified such a way that the noise effect on the guidance system response would be reduced. By using the stochastic stability theory, a modified guidance law, depended on the measurement noises variance, will be proposed such that the line of sight angle rate is stabilized in a finite time. After such a finite-time, no force would be applied to the vehicle actuators. Then the line of sight angle would be a constant one. The proposed method would be used in a two-dimensional numerical example. The effectiveness of the suggested method is shown in the simulation results.