Cellular instability of spherically expanding methanol/air flames was investigated in a constant-volume single chamber cylindrical combustion vessel at initial temperatures of 373-423 K, initial pressures of 1-10 atm and equivalence ratios of 0.7-2.1. Flame morphology shows that the methanol/air flames suffer from cellular instability, especially at 5-10 atm. Stability analysis was performed to determine the logarithmic growth rate of disturbance, the critical Peclet number and the critical flame radius. The influences of initial temperature, initial pressure and equivalence ratio on cellular instability were analyzed to identify the influential factors. Both experimental results and stability analysis indicate cellular instability monotonically increases with increasing temperature or pressure and non-monotonically varies with increasing equivalence ratio. The reduced critical Peclet number and flame thickness slightly destabilize the flame surface as temperature increases. The almost unchanged critical Peclet number and the greatly reduced flame thickness with increasing pressure make the critical flame radius smaller and the flame surface more unstable at high pressures. The monotonically decreased critical Peclet number and the non-monotonically varied flame thickness result in the non-monotonic variation of cellular instability in methanol/air flames versus equivalence ratio. The critical flame radius consequently increases with increasing equivalence ratio under very rich conditions, while the corresponding flame surface becomes more smooth. The non-monotonic variation of cellular instability versus equivalence ratio is anticipated to exist widely in combustion of heavy fuels.