  The sending-or-not-sending (SNS) protocol of the twin-field quantum key
distribution (TFQKD) can tolerant large misalignment error and its key rate can
exceed the bound of repeaterless QKD. But the original SNS protocol requires
the two users to use the same source parameters. Here we propose a general
protocol with asymmetric source parameters and give the security proof of this
protocol. Our general protocol has a much better performance than that of the
original SNS protocol when the channel of the system is asymmetric.
