LED illumination based multispectral imaging is getting much attention in recent years due to its fast computer controlled switching ability, availability of many different LEDs, robustness, and cost effectiveness. In this paper, we propose a system which uses an RGB camera along with two or three combinations of three different types of LEDs in order to acquire multispectral images of six or nine channels. Optimal LED combinations are selected so as to produce accurate estimate of spectral reflectance and/or color. The system is rather simple to realize. Moreover, it is faster as it requires only two or three shots, unlike state of the art multiplexed LED illumination based systems which require as many shots as the number of channels that a system can acquire. The proposed system can be useful in general multispectral imaging applications. The system has been evaluated with both the natural images and paintings. The results from the simulation experiments were promising, indicating the possibility of the proposed system as a practical and feasible method of multispectral imaging.