We propose a new parametrization of the deceleration parameter to study its time-variation behavior. The advantage of parameterizing the deceleration parameter is that we do not need to assume any underlying theory of gravity. By fitting the model to the 157 gold sample supernova Ia data, we find strong evidence that the Universe is currently accelerating and it accelerated in the past. By fitting the model to the 115 nearby and Supernova Legacy Survey supernova Ia data, the evidence that the Universe is currently accelerating is weak, although there is still a strong evidence that the Universe once accelerated in the past. The results obtained from the 157 gold sample supernova Ia data and those from the 115 supernova Ia data are not directly comparable because the two different data sets measure the luminosity distance up to different redshifts. We then use the Friedmann equation and a dark energy parametrization to discuss the same problem. When we fit the model to the supernova Ia data alone, we find weak evidence that the Universe is accelerating and the current matter density is higher than that measured from other experiments. After we add the Sloan Digital Sky Survey data to constrain the dark energy model, we find that the behavior of the deceleration parameter is almost the same as that obtained from parameterizing the deceleration parameter.