Summary: This paper proposes a new $\cal H_{\infty }$ weight learning law for switched Hopfield neural networks with time-delays under parametric uncertainty. For the first time, the $\cal H_{\infty }$ weight learning law is presented to not only guarantee the asymptotical stability of switched Hopfield neural networks, but also reduce the effect of external disturbance to an $\cal H_{\infty }$ norm constraint. An existence condition for the $\cal H_{\infty }$ weight learning law of switched Hopfield neural networks is expressed in terms of strict linear matrix inequality (LMI). Finally, a numerical example is provided to illustrate our results.