Abstract The Leibnitz-Macluarin Method (LMM) via successive differential coefficients has been employed to proffer series solution of the nonlinear equation arising in the convective straight fins with temperature-dependent thermal conductivity problem. Solutions are presented for the dimensionless temperature distribution and fin efficiency of the nonlinear equation. Parametric analyses indicated two dominant non-dimensional parameters describing the thermal conductivity and thermo-geometrical property of fins. The results revealed that increase in the thermal conductivity increases the wall temperature, while increase in the thermo-geometrical parameter reduces the wall temperature, and that fin efficiency is dependent on both the thermal conductivity and thermo-geometrical property. The LMM results compared with previous numerical, HAM, DTM and available analytical results demonstrated excellent agreements.