We consider uplink multi-carrier code-division multiple access (MC-CDMA) systems in a multi-cell environment. It is assumed that all intra-cell users employ Alamouti's simple space-time block coding (STBC), which is known to the base station receiver, but the receiver has no information on whether inter-cell users employ STBC or not. In this case we propose a blind adaptive minimum output energy (MOE) receiver for uplink STBC MC-CDMA, which is designed to perfectly remove the interference from intra-cell users by using the spreading sequence information on all intra-cell users and to reduce the interference from inter-cell users by minimizing the constrained output energy. Analysis and simulation results show that the proposed adaptive receiver has a faster convergence rate and higher steady-state signal-to-interference plus noise ratio (SINR) than a conventional scheme in which only the spreading code information of the desired user is utilized.