Revealing the cosmic hydrogen reionization history is one of the main goals of the modern cosmology. z > 5 quasars (QSOs) have been used as back-lights to investigate the evolution of the intervening intergalactic medium (IGM) during the cosmic reionization since their first discovery. However, due to the small population of luminous QSOs (similar to 130 QSOs known to date), a tight constraint on the reionization history has not yet been placed. In this work, we aim to tighten the constraint using the 93 QSOs (5.5 < z < 7.1) recently discovered in the Subaru High-z Exploration of Low-Luminosity Quasars (SHELLQS) project. This is the largest QSO sample used to constrain the epoch of reionization. We measure the mean IGM Ly alpha transmission and the QSO near-zone size using the UV spectra of these QSOs. The mean IGM Ly alpha transmission rises above zero at z less than or similar to 6, indicating the end of the reionization. The near-zone sizes of the SHELLQs QSOs are consistent with sizes spanned by QSOs of lifetime t(q) similar to 1-100 Myr in simulations. Due to the scatter created by the low signal-to-noise spectra and large Ly alpha redshift uncertainty, we cannot conclude whether the redshift evolution of the near-zone size is affected by the reionization effect.