An extension of sinc interpolation on \(\mathbb{R}\) to the class of algebraically decaying functions is developed in the paper. Similarly to the classical sinc interpolation we establish two types of error estimates. First covers a wider class of functions with the algebraic order of decay on \(\mathbb{R}\). The second type of error estimates governs the case when the order of function's decay can be estimated everywhere in the horizontal strip of complex plane around \(\mathbb{R}\). The numerical examples are provided.