  In this paper, we have considered various dark energy models in the framework
of a non-canonical scalar field with a Lagrangian density of the form ${\cal
L}(\phi, X)=f(\phi)X{\left(\frac{X}{M^{4}_{Pl}}\right)}^{\alpha -1} - V(\phi)$,
which provides the standard canonical scalar field model for $\alpha=1$ and
$f(\phi)=1$. In this particular non-canonical scalar field model, we have
carried out the analysis for $\alpha=2$. We have then obtained cosmological
solutions for constant as well as variable equation of state parameter
($\omega_{\phi}(z)$) for dark energy. We have also performed the data analysis
for three different functional forms of $\omega_{\phi}(z)$ by using the
combination of SN Ia, BAO and CMB datasets. We have found that for all the
choices of $\omega_{\phi}(z)$, the SN Ia $+$ CMB/BAO dataset favors the past
decelerated and recent accelerated expansion phase of the universe.
Furthermore, using the combined dataset, we have observed that the
reconstructed results of $\omega_{\phi}(z)$ and $q(z)$ are almost choice
independent and the resulting cosmological scenarios are in good agreement with
the $\Lambda$CDM model (within the $1\sigma$ confidence contour). We have also
derived the form of the potentials for each model and the resulting potentials
are found to be a quartic potential for constant $\omega_{\phi}$ and a
polynomial in $\phi$ for variable $\omega_{\phi}$.
