At the Earth’s magnetopause, the Kelvin-Helmholtz (KH) instability, driven by the persistent velocity shear between the magnetosheath and the magnetosphere, has been frequently observed during northward interplanetary magnetic field (IMF) periods and considered as one of the most important candidates for transporting and mixing plasmas across the magnetopause. However, how this process interacts with magnetic field fluctuations, which persistently exist near the magnetopause, has been less discussed. Here we perform a series of 2-D fully kinetic simulations of the KH instability at the magnetopause considering a power-law spectrum of initial fluctuations in the magnetic field. The simulations demonstrate that when the amplitude level of the initial fluctuations is sufficiently large, the KH instability evolves faster, leading to a more efficient plasma mixing within the vortex layer. In addition, when the spectral index of the initial fluctuations is sufficiently small, the modes whose wavelength is longer than the theoretical fastest growing mode grow dominantly. The fluctuating magnetic field also results in the formation of the well-matured turbulent spectrum with a -5/3 index within the vortex layer even in the early non-linear growth phase of the KH instability. The obtained spectral features in the simulations are in reasonable agreement with the features in KH waves events at the magnetopause observed by the Magntospheric Multiscale (MMS) mission and conjunctively by the Geotail and Cluster spacecraft. These results indicate that the magnetic field fluctuations may really contribute to enhancing the wave activities especially for longer wavelength modes and the associated mixing at the magnetopause.