In this paper, we propose an on-line writer recognition method for Thai numeral. A handwriting process is characterized by a change of numeral's shape, which is represented by two features, a displacement of pen-point position and an area of triangle determined from the two adjacent points of pen-point position and the origin. First, the above two features are expanded into Fourier series. Secondly, in order to describe feature of handwriting, FIR (Finite impulse response) system having the above Fourier coefficients as input and output of the system is introduced. The impulse response of the FIR system is used as the feature of handwriting. Furthermore, K-L expansion of the obtained impulse response is used to recognize writer. Writer recognition experiments are performed by using 3,770 data collected by 54 Thai writers for one year. The average of Type I (false rejection) error rate and Type II (false acceptance) error rate were 2.16% and 1.12%, respectively.