Laser dynamics have great potential for various applications, ranging from cryptography to microwave photonics and instrumentation. This letter presents a design for achieving high sensitive sensing and measurement using the dynamics of a laser diode (LD) with a dual external cavity. In the design, one cavity is used to control the dynamics, making the LD operate at the period-one (P1) oscillation state, and the other one is associated with the quantities to be measured. The Lang-Kobayashi equations are modified and solved to develop a bifurcation diagram for the design, from which we determine the P1 state and investigate the sensing performance within this state. It is shown that, when operating in P1, the laser intensity exhibits an oscillation with its amplitude modulated by a traditional optical feedback interferometric (OFI) signal (generated with a single cavity and LD operating at the steady state). It is also observed that the modulation depth is remarkably larger than the magnitude of a traditional OFI signal. This leads to a significant increase in the sensitivity of sensing and measurement and hence provides an attractive solution for the detection of very small or weak physical quantities. An experimental system is designed, and the experimental results verify the high sensitive sensing performance of the proposed design.