Amorphous CoFeB films grown on GaAs(001) substrates demonstrating significant in-plane uniaxial magnetic anisotropy were investigated by vector network analyzer ferromagnetic resonance. Distinct in-plane anisotropy of magnetic damping, with a largest maximum-minimum damping ratio of about 109%, was observed via analyzing the frequency dependence of linewidth in a linear manner. As the CoFeB film thickness increases from 3.5 nm to 30 nm, the amorphous structure for all the CoFeB films is maintained while the magnetic damping anisotropy decreases significantly. In order to reveal the inherent mechanism responsible for the anisotropic magnetic damping, studies on time-resolved magneto-optical Kerr effect and high resolution transmission electron microscopy were performed. Those results indicate that the in-plane angular dependent anisotropic damping mainly originates from two-magnon scattering, while the Gilbert damping keeps almost unchanged.