The present disclosure provides a driving method and apparatus of a liquid crystal display apparatus and a liquid crystal display apparatus, and belongs to a liquid crystal display field. The driving method comprises: generating gray scale data of sub-pixels according to received image data; taking a plurality of sub-pixels as a processing unit, generating gray scale voltage polarity signals, which are used for making gray scale voltages of the plurality of sub-pixels tend to zero entirely, respectively corresponding to the gray scale data of the plurality of sub-pixels; outputting the gray scale data and the corresponding polarity signal of the each sub-pixel to a source driver of the liquid crystal display apparatus. The present disclosure may improve display defects caused by turbulence in a common voltage, such as a green attachment, a crosstalk, a flicker, etc.