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In this paper, we present a computational method to solve the fractional Klein-Gordon equation (FKGE). The proposed technique is the grouping of orthogonal polynomial matrices and collocation method. The benefit of the computational method is that it reduces the FKGE into a system of algebraic equations which makes the problem straightforward and easy to solve. The main reason for using this technique is its high accuracy and low computational cost compared to other methods. The main solution behaviors of these equations are due to fractional orders, which are explained graphically. Numerical results obtained by the proposed computational method are also compared with the exact solution. The results obtained by the suggested technique reveals that the method is very useful for solving FKGE.