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Data fitting is the main method of functional data analysis, and it is widely used in the fields of economy, social science, engineering technology and so on. Least square method is the main method of data fitting, but the least square method is not convergent, no memory property, big fitting error and it is easy to over fitting. Based on the orthogonal trigonometric function system, this paper presents a data forward stepwise fitting algorithm. This algorithm takes forward stepwise fitting strategy, each time using the nearest base function to fit the residual error generated by the previous base function fitting, which makes the residual mean square error minimum. In this paper, we theoretically prove the convergence, the memory property and the fitting error diminishing character for the algorithm. Experimental results show that the proposed algorithm is effective, and the fitting performance is better than that of the least square method and the forward stepwise fitting algorithm based on the non-orthogonal function system.