A signal shaping for the bit-interleaved coded modulation (BICM) is considered. Previous work on signal shaped BICM (SBICM) has two problems: (i) It requires an optimization for the linear factors of superposition modulation. The optimization is valid around target SNR. (ii) The binary labeling of signal constellation is not Gray code. To overcome these problems, non-uniform signal labeling for the input signal with Gaussian distribution is considered. We implement the reduction of peak-to-average power ratio (PAPR) by clipping for the largest signal points. From the numerical results, we show that achievable rate of the proposed modulation is larger than that of the previous modulation of SBICM for wide range of SNR, while keeping the expansion of PAPR small. Moreover it is quite close to the coded modulation capacity for wide range of SNR, especially in some SNR region, it is larger than the coded modulation capacity.