Single-molecule spectroscopy on freely-diffusing molecules allows detecting conformational changes of biomolecules without perturbation from surface immobilization. Resolving fluorescence lifetimes increases the sensitivity in detecting conformational changes and overcomes artifacts common in intensity-based measurements. Common to all freely-diffusing techniques, however, are the long acquisition times. We report a time-resolved multispot system employing a 16-channel SPAD array and TCSPC electronics, which overcomes the throughput issue. Excitation is obtained by shaping a 532 nm pulsed laser into a line, matching the linear SPAD array geometry. We show that the line-excitation is a robust and cost-effective approach to implement multispot systems based on linear detector arrays.