Eccentric aiming is a common and general form in radiation thermometry. In such case, the correction of the size-of-source effect (SSE) is different from that under central aiming, under which the SSE has been characterized and can be easily corrected. The present article studies the eccentric SSE model on a polar coordinate, and the calculation of eccentric SSE requires integration. A polynomial is employed, as an approximation instead of an unintegrable item in the model under eccentric aiming to a circle radiation source, to obtain quasi-analytical solutions of the general and specific eccentric SSE functions. The characteristics of eccentric SSE are discussed, and examples of SSE calculation and correction are given. The SSE caused by eccentric aiming in measurements, such as distribution measurements, should be corrected or accounted in uncertainty for high accuracy of measurements, and can be corrected using the quasi-analytical solutions for circle source.