The non-classical light resonance on the cesium D₁ (894.6 nm) line has important applications in solid-state quantum information networks due to its unique advantages. The cesium D₁ line has a simplified hyperfine structure and can be used to realize a light-atom interface. In our previous work, we demonstrated 2.8-dB quadrature squeezed vacuum light at cesium D₁ line in an optical parametric oscillator(OPO) with a periodically poled KTP(PPKTP) crystal. However, the squeezing level is relatively low, and the tunability that has practical significance for squeezed light has not been further investigated. Theoretically, the increase of the transmittance of output mirror and the decrease of the intra-cavity loss of the OPO can improve the squeezing level. Here, we use super-polished and optimal coating cavity mirrors to improve the nonlinear process in OPO. We prepare 447.3 nm blue light from 894.6 nm fundamental light by a second harmonic generation cavity (SHG). The SHG is a two-mirror standing-wave cavity with a PPKTP crystal as the nonlinear medium. The power of generated blue laser is 32 mW when the incident infrared power is 120 mW. Using the blue light to pump an OPO, we achieve quadrature squeezed vacuum light at cesium D₁ line. The OPO is a two-mirror standing-wave cavity with a PPKTP crystal. The threshold of OPO is reduced to 28 mW. The squeezing level of generated quadrature squeezed vacuum light is increased to 3.3 dB when the pump power is 15 mW. Taking into account the overall detection efficiency, the actual squeezing reaches 5.5 dB. We inject a weak signal beam into the OPO cavity to act as an optical parametric amplifier (OPA), and test the tunability of squeezzed light. The blue light and the squeezed light are tuned by using a low-frequency triangular wave signal to scan the Ti: sapphire laser. Gradually increasing the amplitude of the scanning triangle wave signal, the generated bright squeezed light can be continuously tuned over a range around 80 MHz without losing the stability of the whole system. The generated squeezed light offers the possibility for the efficient coupling between the non-classical source and solid medium in the process of quantum interface.