The electromagnetic fields distributed on the surface region of the nanostructure is very important to improve the performance of the sensor. Here, we proposed a highly sensitive sensor based on toroidal dipole (TD) governed by bound state in the continuum (BIC) in all-dielectric metasurface consisting of single non-coaxial core-shell cylinder nanostructure array. The excitation of TD resonance in a single nanostructure is still challenging. The designed nanostructure not only supports TD resonance in a single nanostructure but also has very high Q-factor. More importantly, its electric field distributes at the surface of outer cylinder-shell, which is very suitable for biosensing. To evaluate the sensing performance of our proposed structure, we investigated the sensitivity and the figure of merit (FOM) of nanostructure with different structural parameters. Maximum sensitivity and FOM can reach up to 342 nm/RIU and 1295 when the asymmetric parameter d =10 nm. These results are of great significance to the research of TD resonance and the development of ultrasensitive sensor.