  In this paper, we have proposed a generalized parametrization for the
deceleration parameter $q$ in order to study the evolutionary history of the
universe. We have shown that the proposed model can reproduce three well known
$q$-parametrized models for some specific values of the model parameter
$\alpha$. We have used the latest compilation of the Hubble parameter
measurements obtained from the cosmic chronometer (CC) method (in combination
with the local value of the Hubble constant $H_{0}$) and the Type Ia supernova
(SNIa) data to place constraints on the parameters of the model for different
values of $\alpha$. We have found that the resulting constraints on the
deceleration parameter and the dark energy equation of state support the
$\Lambda$CDM model within $1\sigma$ confidence level at the present epoch.
