This paper presents a hybrid automatic repeat request (HARQ) with variable spreading factor (VSF) suitable for a multicarrer code division multiple access (MC-CDMA). We consider a HARQ based on incremental redundancy (IR) strategy. The throughput of MC-CDMA HARQ is a tradeoff among the frequency diversity gain, the coding gain and the inter-code interference (ICI). In order to effectively exploit the channel frequency-selectivity and the channel coding, the spreading factor is changed between the initial transmission and the succeeding retransmissions. The throughput performance of HARQ with VSF in a frequency-selective Rayleigh fading channel is evaluated by the computer simulation and compared with that with fixed spreading factor (FSF). It is shown that HARQ with VSF can provide better throughput performance than with FSF and is particularly useful when high-level modulation (e.g., 16QAM and 64QAM) is used. The impacts of fading correlation between packet retransmissions and the channel frequency-selectivity on achievable throughput performance are discussed.