We investigate the temporal correlations and multifractal nature of trading volume of 22 liquid stocks traded on the Shenzhen Stock Exchange in 2003. We find that non-universal long memory exhibits size-dependence on the trading volume, while the multifractal nature is independent of the trading volume. No crossover in the power-law dependence of the detrended fluctuation functions is observed. Our results show that the intraday pattern in the trading volume has negligible impact on the long memory and multifractality. We also find that both the long memory and probability distribution of trading volume have important influence on the multifractal nature.