Here, we investigate the effect of inclination angle on the resonant absorption of standing fast kink body waves in the solar coronal loops. To this aim, we consider a typical coronal loop as a straight, zero-$\beta$, nonaxisymmetric and longitudinally stratified cylindrical magnetic flux tube. With the help of connection formulae, we derived and solved numerically the dispersion relation governing the quasi normal kink modes. Consequently, we obtained both the frequencies and damping rates of the fundamental and first-overtone kink modes. We concluded that as the inclination angle of the loop plane increases: (i) the frequencies and their relevant damping rates decrease. (ii) The frequency ratio w2/w1 of the first overtone and its fundamental mode increases. (iii) The ratio of the oscillation frequency to the damping rate remains unchanged.