A novel temperature and strain dual-parameter fiber sensor is proposed, which is constructed via the cascading between a hollow core fiber and a fiber Bragg grating. The hollow core fiber confines the light to transmit inside the air core based on the anti-resonance mechanism and the light satisfying the resonance condition leaks out of the air core, which is indicated as a periodic loss peak in the transmission spectrum. Because the physical mechanisms for hollow core fiber and fiber Bragg grating as well as their spectral responses to external temperature and strain are different, the simultaneous measurement of temperature and strain can be realized based on the coupling matrix. The experimental results show that the temperature sensitivities of hollow core fiber and fiber Bragg grating are 24.55 pm /℃ and 12.76 pm /℃ near 1550 nm wavelength, respectively. In contrast, the strain sensitivities are -0.70 pm/με and 1.02 pm/με, respectively. The proposed dual-parameter sensor is simple in fabrication and has a high measurement accuracy.