Due to the increased rate of information in the present era, local identification of similar and related data points by using neighborhood construction algorithms is highly significant for processing information in various sciences. Geometric methods are especially useful for their accuracy in locating highly similar neighborhood points using efficient geometric structures. Geometric methods should be examined for each individual point in neighborhood data set so that similar groups would be formed. Those algorithms are not highly accurate for high dimension of data. Due to the important challenges in data point analysis, we have used geometric method in which the Apollonius circle is used to achieve high local accuracy with high dimension data. In this paper, we propose a neighborhood construction algorithm, namely Neighborhood Construction by Apollonius Region Density (NCARD). In this study, the neighbors of data points are determined using not only the geometric structures, but also the density information. Apollonius circle, one of the state-of-the-art proximity geometry methods, Apollonius circle, is used for this purpose. For efficient clustering, our algorithm works better with high dimension of data than the previous methods; it is also able to identify the local outlier data. We have no prior information about the data in the proposed algorithm. Moreover, after locating similar data points with Apollonius circle, we will extract density and relationship among the points, and a unique and accurate neighborhood is created in this way. The proposed algorithm is more accurate than the state-of-the-art and well-known algorithms up to almost 8-13% in real and artificial data sets.