Nuclear magnetic resonance (NMR) on Cu nuclei was performed precisely at low temperatures for 2% Zn-doped SrCu2O3 to investigate the critical behavior near the ordering point. From low-field NMR measurements a sequential appearance of the field-induced staggered moments and the magnetic order was observed with the decrease in temperatures. The integral of the NMR spectra was analyzed to extract the information of the critical slowing down.