A new in-fiber Mach-Zehnder interferometer (MZI) based on lateral-offset and peanut shape structure is proposed and demonstrated for the measure of curvature and liquid level. The sensor consists of lateral-offset structure and peanut shape structure. A section of single mode fiber (SMF) is spliced between them. A part of core mode in the single mode fiber is excited to cladding modes by lateral-offset. The cladding modes are re-coupled to the core mode by peanut-shape structure and get interference with the core mode. A high-quality interference spectrum with a fringe visibility of about 12 dB is observed. The effective refractive indices of cladding mode would change with the external environment parameters, which further bring about a shift of the interference fringes. The liquid level or curvature can be measured by record the shift of the valley, because the shift of the valley shows a linear dependence with the variation of the liquid level or curvature theoretically. In the water level experiment, the water level changes from 1.00 to 5.00 cm and the wavelength valley shows a red shift. The sensitivity of the MZI with a length of 6.10 cm is -0.68 nm·cm-1. In the curvature experiment, the curvature changes from 0.3 to 1.2 and the wavelength valley shows a blue shift. The sensitivity of the MZI with a length of 2.10 cm is 22.47 nm·m. The lateral-offset structure and peanut shape structure are spliced to fabricate the MZI. The sensitivity of the MZI is high, especially in the curvature measurement, it is higher than that of other fiber curvature sensors. Moreover the MZI presented in this paper has advantages of low cost and easy fabrication, which can be a potential application in the liquid level and curvature measurement.