A relation between mean velocity and turbulent shear stress has been derived for turbulent boundary layers developed under adverse pressure gradients. The wall law has been obtained by performing a one-dimensional analysis on the turbulent kinetic energy equation with assumptions of local similarity. The analysis relates the diffusional flux to the shear stress gradient. Physical limiting conditions and known experimental results are used to evaluate unknown constants appearing in the derived equation. The resulting wall law is particularly suited for the near-wall treatment in the numerical calculations.