We put forward a dual-mode photonic crystal nanobeam cavity for simultaneous sensing of the refractive index (RI) and temperature (T) designed with the assistance of artificial neural networks (ANNs). We choose the structure of quadratically tapered elliptical holes with a slot to improve the sensitivities of the two modes. To reduce the time consumption of the design, the ANNs are trained to predict the band structure and to inverse design the geometric structure. For the forward prediction and the inverse design neural networks, low mean square errors of 5.1×10-4 and 1.4×10-2 are achieved, respectively. Through a specific design of band properties by the well-trained neural networks, a dual-mode nanobeam sensor with high quality factors of 9.34×104 and 1.55×105 and a small footprint of 23.8×0.7µm2 are designed. The RI and T sensitivities of the air mode are 405 nm/RIU and 40 pm/K, respectively, whereas those of the dielectric mode are 531 nm/RIU and 27 pm/K, respectively. The present work shows significance in further research on the design and applications for dual-mode cavities.