This paper describes a very low complexity Vector Sum Excited Linear Prediction (VSELP) coding algorithm. The method, to be called regular pulse VSELP (RP-VSELP), is based on regular pulse basis vectors with mutually orthonormal property. In this approach, a very efficient vector-sum codebook is constructed from a set of mutually orthonormal regular pulse basis vectors and enables us to simplify the codebook search without degradation of the synthesized speech quality compared with that of the conventional VSELP. The regular pulse basis vectors are explicitly orthonormalized by means of the Gram-Schmidt procedure. To enhance the speech quality of the RP-VSELP speech coder, perceptually weighted distortion measure between the input and the synthesized speech is utilized in an iterative close-loop training process of the regular pulse basis vectors. It is shown that objective speech quality is improved by the training process. Experimental results demonstrate that the proposed method produces the synthesized speech quality comparable to that of the conventional VSELP scheme at the bit-rate of 4.8 kbps. A 4.8 kbps modified RP-VSELP coder has been successfully implemented for a real-time application using a general purpose 16-bit fixed-point digital signal processor.