Based on the time-temperature-transformation interpretation, a new criterion for glass forming ability, Z = [(Tx-Tg)/(Tl-Tg)][(Tl–Tl(c))/(Tl-Tg)]0.556, is proposed, where Tg, Tx, Tl and Tl(c) respectively denote the glass transition temperature, the onset crystallization temperature upon heating, the liquidus temperature and the onset solidification temperature of the liquid upon cooling. The Z parameter jointly considers the stability of the liquid and the devitrification of glassy phases. A non-linear relationship between the parameter Z and the critical glassy size dc has been found to be log (dc)cal = 0.1392 + 17.0616Z - 41.985(Z)2, showing stronger correlation than other earlier reported parameters. The advantage of using Z as a GFA parameter is that it roughly reflects the relative influences of the thermodynamics and kinetics of the systems on glass formation. In addition, the parameter describes the stability of liquid in the course of being quenched from above liquidus temperature.