In this work, a block coupled algorithm for the solution of laminar, incompressible viscoelastic flow problems on collocated grids is presented. The inter-equation coupling of the incompressible Cauchy momentum equations and extra-stress tensor constitutive equation is obtained by deriving a pressure equation in a procedure similar to a SIMPLE algorithm with the Rhie-Chow interpolation technique, and a special treatment of the diffusion term in the momentum equations added by the improved both-sides diffusion (iBSD) technique, recently developed for the finite volume method. Additionally, the velocity field is considered implicitly in the extra-stress tensor constitutive equation by expanding the convective term with a second order Taylor series expansion. All the equations, comprising the continuity, momentum and extra-stress tensor constitutive equations are block-coupled into a single system of equations. The implicitly coupled system of equations is solved by an algebraic multigrid algorithm, which allows to accelerate the calculation process. The performance improvements obtained with the new solver are studied for three 2D viscoelastic flow case studies, and are quantified in terms of number of iterations and CPU time required to reach the predefined convergence criteria. The presented algorithm has been implemented into the open-source computational library foam-extend, a community driven fork of the OpenFOAM software.