Convolutional neural network (CNN)-based filters have achieved great success in video coding. However, in most previous works, individual models are needed for each quantization parameter (QP) band. This paper presents a generic method to help an arbitrary CNN-filter handle different quantization noise. We model the quantization noise problem and implement a feasible solution on CNN, which introduces the quantization step (Qstep) into the convolution. When the quantization noise increases, the ability of the CNN-filter to suppress noise improves accordingly. This method can be used directly to replace the (vanilla) convolution layer in any existing CNN-filters. Compared with VVenC anchor, only one CNN filter is used and achieves about 3.6% BD-rate reduction for random-access configuration. Also, about 0.8% BD-rate reduction is achieved compared with the previous QP-map method.