It is an important task to make predictions of trading volumes of financial indices to market participants. In the present study, we focus on this issue for the Chinese Stock Index 300 (CSI300) spot by exploring the high-frequency one-minute data spanning the launch date of the corresponding futures to two years after all constituent stocks become shortable, a period witnessing expanding trading activities. As the trading volume series is rather irregular, the neural network is considered to tackle the prediction problem. Several questions are pursued, including whether the trading volume could be reasonably predicted using its lags, whether trading volumes of the nearby and first-distant futures could help improve predictions, how complicated the model should be, and whether the model is robust delivering predictions. Our results show that a relatively simple model based upon ten hidden neurons and thirty lags leads to stable and accurate prediction results based on the relative root mean square error measurement. However, further including predictive information from trading volumes of the futures does not benefit predictions. Market participants and policymakers might find results here helpful for trading platform design, system risk monitoring, and price predictions.