Two national horizontal geodetic datums, namely, the Accra and Leigon datum, have been the only available datum used in Ghana. These two datums are non-geocentric and were established based on astro-geodetic observations. Relating these different geodetic datums mostly involves the use of conformal transformation techniques which could produce results that are not very often satisfactory for certain geodetic, surveying and mapping purposes. This has been ascribed to the incapability of the conformal models to absorb more of the heterogeneous and local character of deformations existing within the local geodetic networks. Presently, application of new approaches such as artificial neural network (ANN) is highly recommended. Whereas the ANN has been gaining much popularity to solving coordinate transformation-related problems in recent times, the existing researches carried out in Ghana have shown that only three-dimensional conformal transformation methods have been utilized. To the best of our knowledge, plane coordinate transformation between the two local geodetic datums in Ghana has not been investigated. In this paper, an attempt has been made to explore the plane coordinate transformation performance of two different ANN approaches (backpropagation neural network (BPNN) and radial basis function neural network (RBFNN)) compared with two different traditional techniques (six- and four-parameter models) in the Ghana national geodetic reference network. The results revealed that transforming plane coordinates from Leigon to Accra datum, the RBFNN was better than the BPNN and traditional techniques. Transforming from Accra to Leigon datum, both the BPNN and RBFNN produced closely related results and were better than the traditional methods. Therefore, this study will create the opportunity for Ghana to recognize the significance and strength of the ANN technology in solving coordinate transformation problems.