The unconventional multigap superconductivity in elemental Pb were reported previously by the surface sensitive tunneling experiments as well as predicted by several theory works. To obtain bulk evidence for such multiple gap behavior, the thermodynamic critical-field B_c was measured along three different crystallographic directions ([100], [110], and [111]) in a high-quality Pb single crystal by means of muon spin rotation/relaxation. No difference in temperature evolution of B_c for all three directions was detected. The average reduced gap (α = Δ/k_BT_c = 2.312(3) (Δ is the zero-temperature gap value, and T_c is the transition temperature) was further obtained by employing the phenomenological α model. Our results imply that the elemental Pb is an isotropic superconductor with a single energy gap.