The magnetic properties of YVO3 single crystals have been studied in the temperature range from 350 to 4.2 K and in magnetic fields up to 7 T. It is found that in an applied field less than 4 kOe remarkable magnetization reversals occur at two distinct temperatures: an abrupt switch at Ts=77 K associated with a first-order structure phase transition and a gradual reversal at T*≈95 K without a structural anomaly. Most interestingly, the magnetization always switches to the opposite direction if the crystal is cooled or warmed through Ts and T* in a field less than ∼500 Oe. In higher magnetic fields the magnetization does not change sign but has a minimum at T* and a sudden change at Ts. A possible mechanism for the observed peculiar magnetic behavior is discussed, related to the competition of the single-ion magnetic anisotropy and the antisymmetric Dzyaloshinsky-Moriya interaction accompanied by a change of orbital ordering.