A hybrid Vlasov-fluid model is developed for the magnetized plasma flows in crossed-field plasma sources. In this model, the Vlasov equation with the source term of ionization is used for the ions and neutral atoms, whereas the electron flow is approximated as a fluid. The Vlasov equation is discretized based on the conservative semi-Lagrangian (CSL) method. A high-order scheme is used for the advection operators based on the constrained interpolation profile (CIP) scheme with the weighted essentially non-oscillatory (WENO) limiter. Through several verification tests we confirm that the developed Vlasov equation solver attains the fourth-order of accuracy as designed, and yields non-oscillatory and noiseless distributions. A 1D plasma flow simulation inside a Hall thruster is performed by the hybrid Vlasov-fluid model, and the ionization oscillation is analyzed. The noiseless Vlasov-fluid model reproduces an ionization oscillation with the steady oscillation amplitude within a short simulation period.