In this paper, a new kind of coding scheme, namely unequal-mark-power (UMP), is proposed for asynchronous incoherent optical code division multiple access (OCDMA) systems and their performance analysis is conducted. In our proposed scheme, in contrast to conventional ones, pulses of the optical code, referred to as marks, do not have equal powers and their power levels increase linearly as a function of the order of mark. Marks are placed among chip times in compliance with optical orthogonal codes (OOCs) to benefit from their unique characteristics in asynchronous circumstances as well as their relative ease of analysis. It is demonstrated that under the same power consumption and bandwidth occupation when the noise-level is low, employing UMP could enhance the bit error probability by about 400 times compared to conventional equal-mark-power systems for the code weight of 8. Moreover, it is shown that OCDMA systems employing UMP outperform the ones using equal-mark-power when the noise-level exceeds or equals the average mark power. This achievement is obtained by adding some amplifiers to the structure of ordinary encoders as well as allowing different thresholds for hardlimiters employed in the structure of the receiver accordingly.