With progression of scaling technique in silicon complementary metal-oxide semiconductor (Si-CMOS) process, it is available to produce radio frequency (RF) circuits using Si-CMOS for broadband wireless system, to reduce cost and size of devices. But in contrast, Si-CMOS RF circuit is deteriorated from circuits which use compound semiconductors. In order to reduce RF circuit's requirements, we propose a multi-carrier transmission with constant envelope modulation for high speed wireless system. Modulating method for sub-carrier is minimum shift keying. All sub-carriers are processed individually to reduce operating bandwidth requirement of intermediate frequency devices, and to keep envelope of input signal of power amplifier (PA) constant, so that the requirements of PAs can be reduced. Moreover, to reduce overall RF bandwidth, sub-carriers are allocated with overlaps. In the case of using 4 sub-carriers, we can get 375MHz baseband bandwidth and 2250MHz RF bandwidth, for 2Gbps system. Then the spectral efficiency is 0.89bit/s/Hz. The degradation of bit error rate is negligibly small.