We report results of experimental investigation of the low-frequency noise in the top-gate graphene transistors. The back-gate graphene devices were modified via addition of the top gate separated by 20 nm of HfO2 from the single-layer graphene channels. The measurements revealed low flicker noise levels with the normalized noise spectral density close to 1/f (f is the frequency) and Hooge parameter below 2 x 10^-3. The analysis of the noise spectral density dependence on the top and bottom gate biases helped us to elucidate the noise sources in these devices and develop a strategy for the electronic noise reduction. The obtained results are important for all proposed graphene applications in electronics and sensors.