QR And is the optically brightest supersoft X-ray source, where a massive white dwarf in a close binary accretes material from its companion star via an accretion disc. Based on the photometric observations from the TESS space telescope and the AAVSO data base, 91 eclipse timings were determined. Variations such as flaring activities, depth and profile changes in the primary and the secondary minima, and some short-term irregular fluctuations are found in the TESS light curves, which are interpreted as the activities of the accretion disc and fluctuations of the mass transfer rate. By collecting all available eclipse timings together with those newly determined, we constructed the O-C diagram and analysed the changes in the orbital period. It is discovered that the orbital period is continuously increasing at a rate of P = +3.7(1) × 10−7d · yr−1 = +0.0320(8)s · yr−1. The continuous increase in the orbital period is mainly caused by the mass transfer from the low-mass companion to the white dwarf on its Kelvin-Helmholtz time-scale, while wind mass loss from the accretion disc may also contribute to the period variation. In this scenario, the mass transfer rate of QR And is estimated to be in the range of about 1.2 × 10−7 to 4.2 × 10−7M × yr−1 and the mass-accretion rate is less than 1.6 × 10−7M × yr−1. It can be roughly estimated that QR And may reach to the Chandrasekhar limit in at least 1.5 million yr, then might explode as a type Ia supernova. © 2023 The Author(s) Published by Oxford University Press on behalf of Royal Astronomical Society.