Abstract: We have calculated production cross sections of new superheavy elements with atomic number Z=119, 120 in the fusion-evaporation reactions of ^48\rmCa+^252\rmEs, ^48\rmCa+^257\rmFm, ^49\rmSc+^252\rmEs, ^49\rmSc+^251\rmCf, ^50\rmTi+^247\rmBk, ^50\rmTi+^251\rmCf, ^51\rmV+^247\rmCm, ^51\rmV+^247\rmCf, ^54\rmCr+^243\rmAm, ^54\rmCr+^247\rmCm, ^56\rmMn+^244\rmPu, ^56\rmMn+^243\rmAm, ^60\rmFe+^237\rmNp, ^60\rmFe+^244\rmPu, ^61\rmCo+^238\rmU, ^61\rmCo+^237\rmNp, ^64\rmNi+^231\rmPa, ^64\rmNi+^238\rmU, ^65\rmCu+^232\rmTh, ^65\rmCu+^231\rmPa, and ^68\rmZn+^232\rmThwithin the dinuclear system model systematically. The inner fusion barriers have been extracted from the driving potential and potential energy surface which could be used to predict the relative fusion probability roughly. The influence of mass asymmetry of the colliding partners on the production of new superheavy elements(SHE) has been investigated systematically. It is found that fusion probability increases along with the increasing mass asymmetry of colliding systems. The ^46-50Ti-induced reactions prefer to produce new SHE with Z=119~120. The dependence of production cross-sections of new superheavy elements on the isospin of projectile nuclei has been discussed. The new SHE of ^289-293\rm119 has been predicted as the synthesis cross sections around one picobarn in the ^44,\, 46,\, 48,\, 50\rmTi-induced reactions. Production cross-section of the element^295\rm120 has been evaluated as large as one picobarn in the reactions ^46\rmTi(^251\rmCf, 2n) ^295\rm120 at E^* = 26 MeV. The optimal projectile-target combinations and beam energies for producing new SHE with atomic number Z = 119~120 are proposed for the forthcoming experiments.