  We bring forward a generalized pressure dark energy (GPDE) model to explore
the evolution of the universe. This model has covered three common pressure
parameterization types and can be reconstructed as quintessence and phantom
scalar fields, respectively. We adopt the cosmic chronometer (CC) datasets to
constrain the parameters. The results show that the inferred late-universe
parameters of the GPDE model are (within $1\sigma$): The present value of
Hubble constant $H_{0}=(72.30^{+1.26}_{-1.37})$km s$^{-1}$ Mpc$^{-1}$; Matter
density parameter $\Omega_{\text{m0}}=0.302^{+0.046}_{-0.047}$, and the
universe bias towards quintessence. While when we combine CC data and the $H_0$
data from Planck, the constraint implies that our model matches the
$\Lambda$CDM model nicely. Then we perform dynamic analysis on the GPDE model
and find that there is an attractor or a saddle point in the system
corresponding to the different values of parameters. Finally, we discuss the
ultimate fate of the universe under the phantom scenario in the GPDE model. It
is demonstrated that three cases of pseudo rip, little rip, and big rip are all
possible.
