A new model for pathological vocal fold vibration is proposed. The model simulates asymmetries in mechanical and geometrical properties of vocal fold, which are pathological features in laryngeal diseases. In this study the effect of asymmetry in vocal fold thickness (Lg) on phonation threshold pressure (PTP) of clinical importance is numerically investigated using the model. The results show that the difference between PTP values in an asymmetric case and those in a symmetric case is small over a wide range of Lg. In the asymmetric case the one of smaller Lg between a pair of vocal folds is found more influential to PTP, and clinical significance of PTP-Lg curve is discussed in relation to surgical treatment for voice disorders caused by unilateral vocal fold paralysis. In the symmetric case PTP-Lg curve is characterised by two distinct regions. Theoretical consideration of the curve from the viewpoint of vocal fold vibration reveals an important role of propagating wave velocity in the region of larger Lg.