The sensor based on gold nanocone hexagonal array structure was designed. Gold nanocone array was positioned above a gold film and separated by silica dielectric spacer layer. Finite-difference time-domain simulation was used to discuss theoretically the influence of gold film and dielectric layer thickness on the structure performance. The formation mechanism of three resonance peaks was studied through the electric field distribution. With the increase of the dielectric thickness, the absorption went upwards first and then went downwards. The refractive index sensitivity of the structure and figure of merit (FOM) at the dipole resonance peak can reach 450 nm/RIU and 4.3, respectively. At the peak caused by the plasmon resonance between the gold nanocone array and the gold film, the sensitivity is 275 nm/RIU while the FOM value is 18.3. The results provide a valuable insight into the application of metal nanoarrays in sensors.