Image steganographic methods based on encoder-decoder model with end-to-end network architecture recently have been proposed. However, in steganographic applications, the feature map (called stego matrix) generated by the encoder needs to be rounded as a real stego image for the receiver. The loss of precision by rounding stego matrix leads to the decline in the accuracy of extracted secret messages. The challenge of using end-to-end network to preserve robustness against rounding operation is that it is non-differentiable. In this paper, we propose an anti-rounding image steganography method with separable fine-tuning network architecture which includes the joint training stage (JT-stage) and the separable fine-tuning stage (SF-stage). Firstly, in JT-stage, an embedded generator and a stego matrix extractor are jointly learned without rounding operation. Utilizing concatenation in embedded generator can realistically fuse cover image and secret messages. And the multi-scale fusion block and residual dense block in stego matrix extractor can make secret messages more correctly decoded. Moreover, the discriminator is constructed by generative adversarial nets (GAN) in JT-stage to effectively improve the authenticity and steganalysis security. Then, in SF-stage, the embedded generator is frozen, and the stego matrix is obtained and rounded as a stego image. A stego image extractor is constructed by fine-tuning the layers of the stego matrix extractor to improve the accuracy of message extraction. As the loss will not backpropagate in the embedded generator, the non-differentiability of rounding operation can be offset. Experiments show that the proposed separation fine-tuning network is robust to rounding operation, and effectively reduces the degradation of the image quality and steganalysis performance.