In this work, we focus on the maximal estimates and point-wise convergence for Schrodinger group $e^{itH}$ with potentials in dimension one, where $H=-\Delta+V$. Under some assumptions on potential V, by using the distorted Fourier transform, as well as the function spaces associated to operators, we prove that the maximal operator of $e^{itH}$ is bounded from $H^s$ to $L^q$, as well as the point-wise convergence for initial data $f\in H^s$.
