The effect of misalignment between the magnetic field $magB$ and the angular momentum $Jang$ of molecular cloud cores on the angular momentum evolution during the gravitational collapse is investigated by ideal and non-ideal MHD simulations. For the non-ideal effect, we consider the ohmic and ambipolar diffusion. Previous studies that considered the misalignment reported qualitatively contradicting results. Magnetic braking was reported as being either strengthened or weakened by misalignment in different studies. We conducted simulations of cloud-core collapse by varying the stability parameter $alpha$ (the ratio of the thermal to gravitational energy of the core) with and without including magnetic diffusion The non-ideal MHD simulations show the central angular momentum of the core with $theta=0^circ$ ($Jang parallel magB$) being always greater than that with $theta=90^circ$ ($Jang perp magB$), independently of $alpha$, meaning that circumstellar disks form more easily form in a core with $theta=0^circ$. The ideal MHD simulations, in contrast, show the the central angular momentum of the core with $theta=90^circ$ being greater than with $theta=0^circ$ for small $alpha$, and is smaller for large $alpha$. Inspection of the angular momentum evolution of the fluid elements reveals three mechanisms contributing to the evolution of the angular momentum: (i) magnetic braking in the isothermal collapse phase, (ii) selective accretion of the rapidly (for $theta=90^circ$ ) or slowly (for $theta=0^circ$) rotating fluid elements to the central region, and (iii) magnetic braking in the first-core and the disk. The difference between the ideal and non-ideal simulations arises from the different efficiencies of (iii).
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