A systematic design method for 3-D grid multiscroll chaotic attractors by using staircase nonlinear functions (SNFs) is proposed in this paper. Equations of parameters for 3-D grid multiscroll chaotic attractors are derived in the consideration of the dynamic range for the active device and the number of multiscroll chaotic attractors. 5 x 4 and 4 x 3 of 3-D grid multiscroll chaotic attractors are generated by this method. A chaotic circuit is designed only using current feedback operational amplifiers (CFOAs). The circuit consists of three integrators and two nonlinear circuits. The parameters of the circuit are calculated by the parameters of 3-D grid multiscroll chaotic attractors. The circuit can generate 3-D grid multiscroll chaotic attractors. The central frequency of the circuit is higher with fewer active devices and simpler circuit construction for the good frequency characteristic and port characteristic of the CFOA. Numerical simulation results and the circuit simulation results show that the method is feasible and the designed circuit is correct.