  We analyze the capacity of a simultaneous quantum secure direct communication
scheme between the central party and other $M$ parties via $M+1$-particle GHZ
states and swapping quantum entanglement. It is shown that the encoding scheme
should be secret if other $M$ parties wants to transmit $M+1$ bit classical
messages to the center party secretly. However when the encoding scheme is
announced publicly, we prove that the capacity of the scheme in transmitting
the secret messages is 2 bits, no matter how big $M$ is.
