A pointwise partially hyperbolic diffeomorphism is different from a partially hyperbolic one if the expansion and contraction depend on points. If the system is defined on an open set, then the hyperbolicity may not be uniform. We show that under certain conditions such a suystem has unstable and stable manifolds, and admits a finite or an infinite u-Gibbs measure. If the system is pointwise hyperbolic, then the u-Gibbs measure $\mu$ is an Sinai-Ruelle-Bowen (SRB) measure
or an infinite SRB measure. As applications, we show that some almost Anosov diffeomorphisms and gentle perturbations of Katok's map have the properties.