In this article, a novel fiber-optic axial-strain sensor is proposed and demonstrated to improve the sensitivity based on the tapered-microfiber-assisted Mach-Zehnder interferometer (MZI), which is fabricated by means of the techniques of flame brush, arc-discharged large lateral offset splicing and tapering. The axial-strain response of the tapered microfiber is theoretically studied and experimentally witnessed. The tested results show the wavelength response of axial-strain is strongly related to both the diameter of taper waist and the cavity length. The fivefold enhancement is gained when the diameter is $\sim 24~\mu$ m with an optimized cavity length. The maximum sensitivity of axial-strain reaches −31.25 pm/ $\mu \varepsilon$ with the detection limit of $\sim 0.6~\mu \varepsilon$ . Our sensor has the merits of compactness, high stability and cost-efficiency, which is very promising and potential to the high precision engineering monitoring and measurements.