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We simplified our previously proposed quantum bit commitment (QBC) protocol based on the Mach-Zehnder interferometer, by replacing symmetric beam splitters with asymmetric ones. It eliminates the need for random sending time of the photons; thus, the feasibility and efficiency are both improved. The protocol is immune to the cheating strategy in the Mayers-Lo-Chau no-go theorem of unconditionally secure QBC, because the density matrices of the committed states do not satisfy a crucial condition on which the no-go theorem holds.

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