In order to improve the flatness of the diaphragm and the ability of the diaphragm-based Fabry-Perot fiber acoustics sensor to detect weak acoustics signal, a large area silver diaphragm was fabricated by sputtered. The diaphragm was then transferred to the sensor head with a sacrifice layer. The diaphragm is as thin as 130 nm, while its diameter is 2.5 mm. Experimental result demonstrate that the flatness of the diaphragm is less than 20 μm. The fabricated sensor's sensitivity is about -158 dB (re 1 V/μPa) with a high linear pressure response range of 0.001-1.250 Pa. The noise equivalent acoustic signal level of 419 μPa·Hz^-0.5 at 1 kHz. The sensor exhibits a flat frequency response in the range of 0.1 kHz to 3 kHz. The diaphragm's flatness is improved by the proposed method and the fabricated sensor is suitable to be useful for highly sensitive measurement of the weak pressure and sound field.