Within the nonlinear relativistic mean field (NL-RMF) model, we show that both the pressure of symmetric nuclear matter at supra-saturation densities and the maximum mass of neutron stars are sensitive to the skewness coefficient J0 of symmetric nuclear matter. Using experimental constraints on the pressure of symmetric nuclear matter at supra-saturation densities from flow data in heavy ion collisions and the astrophysical observation of a large mass neutron star PSR J0348+0432, with the former favoring a smaller J0 while the latter a larger J0, we extract a constraint of −494MeV ≤ J0 ≤ −10MeV based on the NL-RMF model. This constraint is compared with the results obtained in other analyses.