To reconstruct a radioactive tracer distribution with positron emission tomography (PET), the background attenuation correction is needed to eliminate image artifacts. Recent research shows that time-of-flight (TOF) PET data determine the attenuation sinogram up to a constant, and its gradient can be computed using an analytic algorithm. In this paper, we study a direct estimation of the sinogram only from TOF PET data. First, the gradient of the attenuation sinogram is estimated using the aforementioned algorithm. Then, a relationship is established to link the differential attenuation sinogram and the underlying attenuation background. Finally, an iterative algorithm is designed to determine the attenuation sinogram accurately and stably. A 2D numerical simulation study is conducted to verify the correctness of our proposed approach.