In this article, we study the discrete version of Legendre spectral and iterated Legendre spectral techniques to solve the second kind Hammerstein type weakly singular integral equations. To obtain the convergence analysis, we use the appropriate numerical quadrature rule and obtain the order (Formula presented.) in discrete Legendre spectral method. If the quadrature rule is minimal, i.e. the number of quadrature nodes and the dimension of the approximating subspace are same, then the optimal rate is obtained (Formula presented.) in iterated form of discrete Legendre spectral collocation method in (Formula presented.) norm and uniform norm. Numerical aspects are given to verify the hypothetical results. © 2021 Informa UK Limited, trading as Taylor & Francis Group.