We detail the design, construction and performance of the second generation UCL time-resolved optical tomography system, known as MONSTIR II. Intended primarily for the study of the newborn brain, the system employs 32 source fibres that sequentially transmit picosecond pulses of light at any four wavelengths between 650 and 900 nm. The 32 detector channels each contain an independent photo-multiplier tube and temporally correlated photon-counting electronics that allow the photon transit time between each source and each detector position to be measured with high temporal resolution. The system's response time, temporal stability, cross-talk, and spectral characteristics are reported. The efficacy of MONSTIR II is demonstrated by performing multi-spectral imaging of a simple phantom.