The goal of this study was to exploit the excellent spatial resolution characteristics of a position-sensitive silicon photomultiplier (SiPM) and develop a high-resolution depth-of-interaction (DOI) encoding positron emission tomography (PET) detector module. The detector consists of a 30  ×  30 array of 0.445  ×  0.445  ×  20 mm³ polished LYSO crystals coupled to two 15.5  ×  15.5 mm² linearly-graded SiPM (LG-SiPM) arrays at both ends. The flood histograms show that all the crystals in the LYSO array can be resolved. The energy resolution, the coincidence timing resolution and the DOI resolution were 21.8  ±  5.8%, 1.23  ±  0.10 ns and 3.8  ±  1.2 mm, respectively, at a temperature of -10 °C and a bias voltage of 35.0 V. The performance did not degrade significantly for event rates of up to 130 000 counts s^-1. This detector represents an attractive option for small-bore PET scanner designs that simultaneously emphasize high spatial resolution and high detection efficiency, important, for example, in preclinical imaging of the rodent brain with neuroreceptor ligands.