We have investigated the substitution effect of Eu on the superconductivity in La2-xEuxO2Bi3Ag0.6Sn0.4S6. Recently, we reported an observation of superconductivity at 0.5 K in a layered oxychalcogenide La2O2Bi3AgS6. The Sn doping at the Ag site was found to raise the superconducting transition temperature, Tc to 2.5 K in La2O2Bi3Ag0.6Sn0.4S6. To further improve the superconducting properties, we have partially substituted Eu for the La site to increase the chemical pressure in La2-xEuxO2Bi3Ag0.6Sn0.4S6 (x = 0.1 to 0.6). With the increase in Eu concentration, x, the lattice constant a was found to shrink, while the lattice constant c was marginally shortened, which suggests that the chemical pressure induced by the Eu doping is uniaxial along the a-axis. Tc was observed to increase with increasing x up to x = 0.4, further decreasing for higher Eu concentrations of x = 0.5 and 0.6. From the magnetic susceptibility and resistivity measurements, the bulk nature of superconductivity has been observed for x = 0.1 to 0.5 with Tc = 2.5 to 4.0 K, respectively. The upper critical field (Bc2) was noted to be 3.5 T for x = 0.4, which also has the highest Tc.