In this work, we report the influence of ambient refractive index changes on the output power of a multimode fiber with long period grating (LPG) written on it. It is seen experimentally that the cladding mode profiles of such a LPG sensor is very sensitive to the change in refractive index of the surrounding medium. In order to study the influence of ambient refractive index, we have utilized LPG with different periods (100 micrometer, 250 micrometer and 500 micrometer) and multimode fibers with different core diameter (200 micrometer and 400 micrometer). The variation in the output power as a function of different period and fiber dimensions is also investigated. In addition to the many advantages of optical sensors, the unique features such as low insertion loss, low back reflection and easy fabrication of LPG sensors make the present measurement system simple, reliable and accurate for measuring refractive index of the medium surrounding the cladding.