Single C-vacancy and pyridine-like N3 defect are usually formed on the single-walled carbon nanotube (SWCNT) and they have unique properties for potential applications. In this paper, we use density functional theory to investigate the discrepancies of such two structures from the geometric and electronic aspects. Our results indicate that the existed single vacancy in the SWCNT can lead to somewhat electron localization because of the lone pair electrons; while the N3 embedded SWCNT ( N3-SWCNT) has stronger chemical reactivity and electron localization than the single vacancy SWCNT (SV-SWCNT) due to the great charge transfer between N3 group and C atom on the tube sidewall. Through the investigation of Ag-doping on the above two nano-structures, we found that the single Ag atom is much more stably adsorbed on the N3- SWCNT sidewall compared with SV-SWCNT, forming higher binding energy and higher electron transfer. Our calculation would shed light on the physicochemical property of SWCNT-based material and thus extend their potential applications in many fields.