We develop an optimum code allocation scheme by investigating the peak to average power ratio (PAPR) characteristic of a down-link multi-carrier (MC)-CDMA system using Walsh-Hadamard code. It is shown that PAPR of a MC-CDMA system is highly dependent upon the selection of code combination. Based on this fact, we develop the allocation method which minimizes PAPR according to the number of active users. In addition, an efficient suboptimum code combination search scheme is also proposed for near minimum PAPR.