The current analysis deals with the transient analysis of a sigmoid functionally graded material hyperbolic paraboloid shell panel under thermo-mechanical loading. The material properties those depend on temperature at any location along the length are estimated according to sigmoid volume fraction in conjunction with the Mori–Tanaka micromechanical model. The first-order shear deformation theory (FSDT) combined with Sanders’ first approximation shell theory and eight-noded isoparamteric element having five degrees of freedom per node is used to build the finite element formulation for the present investigation. The transient response for the sigmoid functionally graded material (S-FGM) hyperbolic parabolic shell panel (HPSP) is obtained using Hamilton’s principle combined with Newmark constant acceleration technique. The accuracy of the current finite element method is established by matching the results obtained with the benchmark example. New results are present to investigate the influence of material gradient index and radius of curvature on the transient response of HPSP.