Background: Outlier detection has recently become an important problem in many industrial and financial applications. The proposal in this paper is based on detect an outlier in circular data by the local density factor (LDF). The name of local density estimate (LDE) is justified by the fact that we sum over a local neighborhood compared to the sum over the whole circular data commonly used to compute the kernel density estimate (KDE). Methods: We discuss new techniques for outlier detection which find the outliers by comparing the local density of each point to the local density of its neighbors in circular data. In our experiments, we performed simulated two data sets generated a set of circular random variables from von Mises distribution with different sizes and each have two clusters non-uniform density and sizes, then we used (LDF) algorithm. Results: The results show that (LDF) algorithm detect an outliers in five samples named as A, B, C, D and E using von Mises concentration parameter (k( and suitable smoothing parameter (h) for two different datasets. Conclusion: It can be concluded from the present study that the proposed method (LDF method) can be very successful for the outlier detection task in circular data.