We consider the design of the equal gain precoder in flat-fading and limited feedback multiple-input multiple-output (MIMO) systems. The advantage of the equal gain precoder based on the scalar quantization (SQ) is that it is easier to encode the feedback information and no need to construct codebook in advance. In the sort of precoder, the bit allocation methods will dominate the system performance. In this paper, we explore an efficient bit allocation algorithm for the scalar quantized equal gain precoder. The proposed bit allocation scheme can improve the performance of the straightforward scalar quantized equal gain precoder. Compared to the optimal bit allocation scheme with exhaustive search, the proposed algorithm greatly reduces the computational complexity while the performance is near to the optimal scheme.