The transport properties in ultrasmall single-wall carbon nanotubes (SWCNTs) under tensile strain have been theoretically investigated. The regular negative differential resistance (NDR) induced by the strain undergoes a process from enhancement to weakening in the zigzag (3,0) SWCNT. The NDR achieves maximum with applying 4% tensile strain. Compared to the case of (3,0) SWCNT, that NDR cannot be manipulated by applying strain clearly in (4,0) and (5,0) ultrasmall SWCNTs with tensile strain lower than 10%. It proposes this strain-induced NDR effect to demonstrate the possibility of finding potential applications in SWCNT-based NDR nanodevices such as in memory devices, oscillators and fast switching devices.