We have investigated systematically by magnetization measurements the penetration depth λ of HgBa 2 CuO 4 + δ with doping 0.1≤δ≤0.3, ranging from the underdoped region of δ<0.22 to the overdoped region of δ>0.22. The penetration depth was found to vary with temperature quadratically for the underdoped samples below the transition temperature (T c ) over the entire temperature region examined, while linearly for the optimally doped and overdoped samples below 0.5 T c . The observation suggests that the temperature dependence of λ is affected by doping in a complex way and its inference to the pairing symmetry should be taken only with extreme care.