Coupling at the interfaces between antiferromagnetic and ferromagnetic constituents is known to be responsible for the exchange-bias effect, where external stimulus like temperature, electric or magnetic fields are supposed to influence the associated phenomenology. In this paper, we prepare the polycrystalline Co2TiO4 and investigate its temperature- and field-dependent magnetization, from which an unusual exchange-bias effect associated with magnetic reversals is extracted. At low temperature, a continuous crossover from negative to positive exchange-bias fields can be obtained with increment of the cooling magnetic field, showing a magnetically tunable effect. The bipolar switching of exchange-bias field in this compound depends on the relative orientation between Co2+ and [Co3+Ti3+] magnetic moments.