In this paper, we provide a method to recover off-the-grid frequencies of a signal in two-dimensional (2-D) line spectral estimation. Most of the literature in this field focuses on the case in which the only information is spectral sparsity in a continuous domain and does not consider prior information. However, in many applications such as radar and sonar, one has extra information about the spectrum of the signal of interest. The common way of accommodating prior information is to use weighted atomic norm minimization. We present a new semidefinite program using the theory of positive trigonometric polynomials that incorporate this prior information into 2-D line spectral estimation. Specifically, we assume prior knowledge of 2-D frequency subbands in which signal frequency components are located. Our approach improves the recovery performance compared with the previous work that does not consider prior information. Through numerical experiments, we find out that the amount of this improvement depends on prior information we have about the locations of the true frequencies.