Abstract <p> A weak conical dual greedy algorithm is considered, which is a generalization of the conical greedy algorithm, applicable in Hilbert space, to a wider class of Banach spaces. This algorithm approximates an arbitrary element of the space by a combination of elements of a positive complete dictionary with nonnegative coefficients. The convergence of the algorithm and a bound for the rate of convergence for elements in the convex hull of the dictionary are proved. </p>