Equilibrium points of cellular neural networks (CNNs)provide theoretical support for associative memories. However，the CNNs with high gain activation function have not been studied. Unity gain function is included by high gain activation function. Therefore，there are wide applications for high gain activation function. In this paper，the number of equilibrium points of each cell in CNNs with high gain activation function is considered. Some stable conditions about CNNs are obtained by use of the relationship between connection parameters. From these stable conditions and inputs and outputs of a CNN，the regions of values of parameters in CNNs can be gotten. Meanwhile，the number of equilibrium points of every cell can be obtained，where the number is less than 2 δ. Some numerical simulations are presented to support the effectiveness of the theoretical analysis.