Squeezed state of light is an important resource of optical measuerments below the shot noise limit and has been used to improve measurement sensitivity in many areas such as gravitational wave detection, especially in audio frequency region. Compared with the high-frequency squeezed states, the generation of the low-frequency squeezed states is more difficult, because it is limited by several technical noise sources. In this paper we report the observation of more than 2 dB of vacuum squeezing at 1064 nm in the gravitational-wave detection band down to 3 kHz with a double-resonant optical parametric oscillator (OPO). The OPO has a configuration of linear cavity consisting of an input coupling mirror with a transmission of 11% at 532 nm and an output coupling mirror with the transmission of 12% at 1064 nm. The nonlinear materials in the OPO is type-I periodically poled potassium titanyl phosphate (PPKTP) crystal which is chosen for this experiment due to its higher nonlinearity, broader phase matching temperature, and smaller photo-thermal effect. The OPO is pumped by the light of 532 nm from Nd: YVO4/KTP solid-state laser of maximum optical power 3 W. To avoid various noise coupled from the seed beam, the OPO is seeded by vacuum fluctuations instead of coherent field at the fundamental wavelength (1064 nm). A Pound-Drever-Hall (PDH) locking scheme is used to lock the OPO cavity length with the signal derived from the reflected pump beam, so as to lock the pump field and also lock the fundamental field. To make both the pump and seed beams resonant simultaneously, the temperature of the PPKTP is carefully adjusted. The squeezed state can be detected on a homodyne detection by interfering it with the local oscillator (LO) and detected by a balanced detector with two photodiodes (EXT500 T) but having the same quantum efficiency of 86% at 1064 nm. The subsequent electronic noise is analyzed with a low-frequency spectrum analyzer, which shows that the audio noise sources from lab enviroment, locking quality, escape efficiency, propagation loss, homodyne efficiency and detection efficiency have effect on the squeezing pruced by an OPO.