Existing deep learning-based seismic data denoising methods mainly involve supervised learning, in which a denoising network is trained using a large amount of noisy input/clean label pairs. However, the scarcity of high-quality clean labels in practice limits the applicability of these methods. Recently, the blind spot (BS) strategy in the field of image processing has attracted extensive attention. Under the assumption that the noise is statistically independent and the true signal exhibits some correlation, the BS strategy allows us to estimate a denoiser from the noisy data itself. In this article, we study the application of the BS strategy to the random noise attenuation of seismic data and propose an unsupervised blind spot network (BSnet) method. Specifically, considering the characteristics of the random noise, we improve the commonly used Unet network and design two types of randomly mask operators to deal with Gaussian white noise and bandpass noise. Synthetic and real data experiments validate the effectiveness of the proposed method.