We have investigated the interaction of dodecyltrimethylammonium chloride (DoTA) micelle with weak polyelectrolytes, poly(acrylic acid) and poly(methacrylic acid). Anionic as well as un-ionized forms of the polyelectrolytes were studied. Polyelectrolyte-surfactant complexes were formed within 5-11 ns of the simulation time and were found to be stable. Association is driven purely by electrostatic interactions for anionic chains whereas dispersion interactions also play a dominant role in the case of un-ionized chains. Surfactant headgroup nitrogen atoms are in close contact with the carboxylic oxygens of the polyelectrolyte chain at a distance of 0.35 nm. In the complexes, the polyelectrolyte chains are adsorbed on to the hydrophilic micellar surface and do not penetrate into the hydrophobic core of the micelle. Polyacrylate chain shows higher affinity for complex formation with DoTA as compared to polymethacrylate chain. Anionic polyelectrolyte chains show higher interaction strength as compared to corresponding un-ionized chains. Anionic chains act as polymeric counterion in the complexes, resulting in the displacement of counterions (Na+ and Cl-) into the bulk solution. Anionic chains show distinct shrinkage upon adsorption onto the micelle.Detailed information about the microscopic structure and binding characteristics of these complexes is in agreement with available experimental literature.