Nowadays, the Fuzzy C-means method has become one of the most popular clustering methods based on minimization of a criterion function. However, the performance of this clustering algorithm may be significantly degraded in the presence of noise. This paper presents a robust clustering algorithm called Bilateral weighted Fuzzy Cmeans (BWFCM). We used a new objective function that uses some kinds of weights for reducing the effect of noises in clustering. Experimental results using, two artificial datasets, five real datasets, viz., Iris, Cancer, Wine, Glass and a speech corpus used in a GMM-based speaker identification task show that compared to three well-known clustering algorithms, namely, the Fuzzy Possibilistic C-means, Credibilistic Fuzzy C-means and Density weighted Fuzzy C-means, our approach is less sensitive to outliers and noises and has an acceptable computational complexity.