We study the representation theory of the Bershadsky-Polyakov algebra W k = W k (sl 3 , f θ ). In particular, Zhu algebra of W k is isomorphic to a certain quotient of the Smith algebra, after changing the Virasoro vector. We classify all modules in the category O for the Bershadsky-Polyakov algebra W k for k = −5/3, −9/4, −1, 0. In the case k = 0 we show that the Zhu algebra A(W k ) has 2-dimensional indecomposable modules.