We study the kilohertz quasi-periodic oscillations (kHz QPOs) in neutron star low-mass X-ray binaries (LMXBs) with a new magnetohydrodynamics (MHD) model, in which the compressed magnetosphere is considered. The previous MHD model is reexamined and the relation between the frequencies of the kHz QPOs and the accretion rate in LMXBs is obtained. Our result agrees with the observations of six sources (4U 0614+09, 4U 1636-53, 4U 1608-52, 4U 1915-15, 4U 1728-34, and XTE 1807-294) with measured spins. In this model, the kHz QPOs originate from the MHD waves in the compressed magnetosphere. The single kHz QPOs and twin kHz QPOs are produced in two different parts of the accretion disk and the boundary is close to the corotation radius. The lower QPO frequency in a frequency-accretion rate diagram is cut off at a low accretion rate and the twin kHz QPOs encounter a top ceiling at a high accretion rate due to the restriction of the innermost stable circular orbit.