When we have two data sets and want to find the nearest neighbour of each point in the first dataset among points in the second one, we need the all nearest neighbour operator. This is an operator in spatial databases that has many application in different fields such as GIS and VLSI circuit design. Existing algorithms for calculating this operator assume that there is no pre computation on these data sets. These algorithms has o(n*m*d) time complexity where n and m are the number of points in two data sets and d is the dimension of data points. With assumption of some pre computation on data sets algorithms with lower time complexity can be obtained. One of the most common pre computation on spatial data is Delaunay graphs. In the Delaunay graph of a data set each point is linked to its nearest neighbours. In this paper, we introduce an algorithm for computing the all nearest neighbour operator on spatial data sets based on their Delaunay graphs. The performance of this algorithm is compared with one of the best existing algorithms for computing ANN operator in terms of CPU time and the number of IOs. The experimental results show that this algorithm has better performance than the other.