Free-space optical links are vulnerable to atmospheric fading and pointing errors. When a laser beam wanders, most previous works model the random radial displacement distance of the pointing error as a Rayleigh distributed random variable. However, for a non-ideally fast-tracked laser beam, the radial displacement distance at the receiver aperture may not obey the Rayleigh distribution, since the displacements in vertical and horizontal directions may not always follow a zero-mean Gaussian distribution. In this paper, we generalize a widely used pointing error model by assuming that the radial displacement distance follows a Rician distribution and derive a closed-form probability density function (PDF) of the generalized pointing error model. Furthermore, we derive closed-form PDFs for the composite lognormal and Gamma-Gamma turbulence channels using this generalized pointing error model. Error rate performance is also studied for an on-off keying signaling system with intensity modulation and direct detection in the presence of this generalized pointing error.