In this paper, we propose a new projection method. We consider the noise suppression problem under the condition that there are two types of noise. One is the random noise which is treated as a full-rank process. The other is the structured noise which is treated as a low-rank process. For suppression of these noises, the orthogonal projection and the oblique projection have been known. The orthogonal projection can effectively suppress the random noise but can not remove the structured noise. On the other hand, the oblique projection can perfectly remove the structured noise but enhances the random noise. Therefore, we represent the new projection which is a weighted combination of the orthogonal projection and the oblique projection. We refer to the projection method as biased projection. Moreover, we propose a determination method of the combination weight. A comparison with the other projections shows the efficiency of the biased projection.