As the demand of important non-renewable oil and gas resources increase, distributed optical fiber acoustic sensing systems have been widely used in the acquisition of vertical seismic profile (VSP) data relying on its various advantages. The complicated underground environment produces many types of noise with strong energy. Meanwhile, the effective information is absorbed by the formation reflection and refraction, resulting in obvious energy loss and aliased frequency characteristics. Satisfactory processing results and quality cannot be achieved through traditional denoising methods. In recent years, rapidly developed deep learning methods with attention mechanism have greatly attracted researchers. Noise reduction and signals reconstruction technologies with multiple attention mechanism under the framework of joint-domain features is becoming an important development direction of DAS data processing. Attention mechanism can help the network ignore useless information and pay attention to useful information like humans. This paper presents a novel learnable dual attention fusion network (LDAFNet). It combines local and patch-based non-local attention mechanisms together based on the ResBlock modules and makes the extraction process of the network learnable and selective according to different signals or noise. In addition, the novel network can focus on the local complex information and those from the global level. Meanwhile, the residual learning strategy is used to simplify the training process to gradually establish the best mapping under the guidance of L2 loss function. All the experimental results of the simulation and actual records show that our novel network has better denoising and effective signals restoration ability. It can clearly recover the upward and downward wave fields and attenuate different types of noise with less effective energy loss.