A linear perturbation analysis is made on convective instability of the oceanic lithosphere to understand the occurrence of subduction on the Earth. The oceanic lithosphere is modeled by the upper part of top thermal boundary layer in a convecting Newtonian temperature‐dependent viscosity fluid. Thickening of oceanic lithosphere with its age due to cooling at the surface is modeled by thickening of the thermal boundary layer with time; its thickening rateL˙is a measure of the rate with which temperature in the thermal boundary layer decreases with time and hence is a measure of the rate with which viscosity in the thermal boundary layer increases with time. The linear perturbation analysis shows the possible excitation of plural eigenmodes to give rise to an instability in the thermal boundary layer depending on a threshold valueRcof the local Rayleigh numberRof the thermal boundary layer. Further,Rcis shown to be a linearly increasing function ofL˙, which is treated as a free parameter. From estimates ofRandL˙appropriate for the major oceanic lithosphere (denoted asRobsandL˙obs, respectively), I find thatRc(L˙= 0)