In this study, a SPICE model for negative capacitance vertical nanowire field-effect-transistor (NC VNW-FET) based on BSIM-CMG model and Landau-Khalatnikov (LK) equation was presented. Suffering from the limitation of short gate length there is lack of controllable and integrative structures for high performance NC VNW-FETs. A new kind of structure was proposed for NC VNW-FETs at sub-3nm node. Moreover, in order to understand and improve NC VNW-FETs, the S-shaped polarization-voltage curve (S-curve) was divided into four regions and some new design rules were proposed. By using the SPICE model, device-circuit co-optimization was implemented. The co-design of gate work function (WF) and NC was investigated. A ring oscillator was simulated to analyze the circuit energy-delay, and it shown that significant energy reduction, up to 88%, at iso-delay for NC VNW-FETs at low supply voltage can be achieved. This study gives a credible method to analysis the performance of NC based devices and circuits and reveals the potential of NC VNW-FETs in low-power applications.