We investigated the width (N) dependence on the magnetization of N-ZSiC NR with electron and hole doping on the basis of systematic DFT calculations. The critical values of the upper and down critical concentration to give the maximum and zero magnetic moment at edge Si/C atoms by electron/hole doping ($x_{up,e}$, $x_{down,e}$, $x_{up,h}$, and $x_{down,h}$) depend on the width of N-ZSiC NR. Moreover, due to $x_{up,e};{ eq};x_{up,h}$ and $x_{down,e};{ eq};x_{down,h}$, the electron and hole doping effect are asymmetry, i.e, the critical electron doping value ($x_{down,e}$) is smaller than the critical hole doping value ($x_{down,h}$) and is almost independent of the width of NZSiC NR though the other critical values of the electron and hole doping that influence the magnetization of N-ZSiC NR depend on the width. It was also found that at $x_{down,e}$ or $x_{down,h}$ doping, the N-ZSiC NR turns into unusual non-magnetic metallic state. The magnetic behavior was discussed based on the band structures and projected density of states (PDOS) under the effect of electron/hole doping.