The refractive index of Z-cut quartz under magnetically driven quasi-isentropic compression is researched by using the pulsed power generator CQ-4. Its velocities of interface between the aluminum panel and the window are measured by a four-channel dual laser heterodyne velocimeter, which is operated at an incident laser wavelength of 1550 nm. The history profile of magnetic pressure on the electrodes is obtained by a backward integration calculation of the aluminum/LiF interface velocity. And then the pressure history profile is used in the LS-DYNA simulation to get the true particle velocity of the aluminum/quartz interface. Combining with the apparent particle of aluminum/quartz interface which is obtained from experiments, a continuous index of refraction in Z-cut quartz has been obtained at up to a pressure of 14.55 GPa as the longitudinal stress is gradually increased to its elastic limit. The relation between the apparent particle and true particle velocities can be fitted by a polynomial, and the required derivative obtained by differentiation of that polynomial. Refractive index determined from the linear fitting parameters is n=1.087 ( 0.008)+0.4408 /0, which agrees well with the previous shock results. Results from polarizability analysis suggest that the temperature and loading path should have less effect on the refractive index of Z-cut quartz within its elastic limit.