In the Gaussian-modulated coherent states (GMCS) quantum key distribution (QKD), basis choice is a necessary procedure if homodyne detector is used. However, finite bandwidth of the digital-to-analog convertor (DAC) at the receiver's side may lead to the imperfection of the basis choice, namely, maybe Bob can not exactly modulate 0 or π 2 on the phase modulator to implement the homodyne detection.We investigate the GMCS QKD scheme with imperfect basis choice under realistic conditions of quantum channel and detector.We show that the imperfection causes a misestimate of the transmittance and the excess noise, the secret key rate and the security of the system are dramatically decreased consequently. To achieve a reliable quantum key distribution, a security bound to the noise induced by the imperfect basis choice is derived for reverse reconciliation and homodyne detector. Besides, we propose and demonstrate a countermeasure against the noise due to imperfect basis choice.

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