Secret group key generation based on physical layer in wireless communications has a lot of practical applications. A few studies focused on the theoretical bounds of the secret key rate based on the sets of received signals rather than a particular secret key generation scheme. We propose a secret group key generation scheme for an arbitrary number of legitimate nodes, n, in mesh topology in the presence of a passive eavesdropper. In the scheme, after general pilot signal transmissions at all nodes, each node broadcasts a weighted combination of its received signals with optimized coefficients, so that legitimate nodes can obtain the information of channels used for group key generation while the eavesdropper cannot. We also apply different quantization schemes for quantizing and encoding the estimated channels into keys. To provide detailed transmissions and processing steps of group key generation, we also describe the proposed scheme for 4-node mesh topology case. The simulation results show that the proposed scheme achieves a higher secret group key rate and a lower key disagreement rate than a benchmark scheme.