We present an analysis of high time resolution spectra of the chemically peculiar Ap star HD 213637. The star shows rapid radial velocity variations with a period close to the photometric pulsation period. Radial velocity pulsation amplitudes vary significantly for different rare earth elements. The highest pulsation amplitudes belong to lines of TbIII ~360 m/s, PrII ~250 m/s and PrIII ~230 m/s . We did not detect any pulsations from spectral lines of EuII and in Halpha, in contrast to many other roAp stars. We also did not find radial velocity pulsations using spectral lines of other chemical elements, including Mg, Si, Ca, Sc, Cr, Fe, Ni, Y and Ba. There are phase shifts between the maxima of pulsation amplitudes of different rare earth elements and ions, which is evidence of an outwardly running magneto-acoustic wave propagating through the upper stellar atmosphere.