A method for realizing wavelet transform (WT) is presented, in which the WT is synthesized by a bank of switched-current (SI) filters whose impulse responses are the basic wavelet function and its dilations. SI circuits are well suitable for this application since the dilation constant across different scales of the transform can be precisely implemented and controlled by the sampling frequency. In this article, the wavelet base is approximated by a systematic algorithm with all the involved approximation parameters taken into account. Also, the SI filter employing the followthe-leader feedback (FLF) multiple-loop feedback (MLF) structure is proposed to synthesize the approximation function. The Gaussian wavelet is selected as an example to illustrate the design procedure. Simulation results indicate that the proposed method has the merits of high approximation accuracy, strong stability and low sensitivity.