In this paper,~we use the fixed point index theory to show the existence of multiple positive solutions for a class of second-order Robin problems $$ \left\{\begin{array}{ll} u''(t)-k^{2}u(t)+\lambda f(u(t))=0, ~~\ \ \ t\in (0,1),~~k\neq0,\\[2ex] u'(0)=0,~~u(1)=0 \end{array} \right. $$ where~$f:[0,\infty)\rightarrow [0,\infty)$~is continuous and has multiple zeros,~$\lambda >0$~is a parameter.
