A construction scheme of variable-weight optical orthogonal codes (VW-OOCs) for asynchronous optical code division multiple access (OCDMA) system is proposed. According to the actual situation, the code family can be obtained by programming in Matlab with the given code weight and corresponding capacity. The formula of bit error rate (BER) is derived by taking account of the effects of shot noise, avalanche photodiode (APD) bulk, thermal noise and surface leakage currents. The OCDMA system with the VW-OOCs is designed and improved. The study shows that the VW-OOCs have excellent performance of BER. Despite of coming from the same code family or not, the codes with larger weight have lower BER compared with the other codes in the same conditions. By taking simulation, the conclusion is consistent with the analysis of BER in theory. And the ideal eye diagrams are obtained by the optical hard limiter.