The penetration depth and the fueling efficiency of the supersonic molecular beam injection (SMBI) are affected by both the intrinsic parameters of the SMBI and the parameters of background plasma. The purpose of the present paper is to explore the possible methods of improving the fueling efficiency of SMBI by varying the beam parameters. The penetration depths and the transport processes of SMBI with different beam densities and different beam widths are studied using the trans-neut module of the three-dimensional (3D) edge turbulence simulation code BOUT++. In our present study, the number of the injected molecules per unit time the injection speed and the injected flux are kept constant throughout the SMB fueling process, but the beam density and beam width are adjusted. The simulation is based on the real magnetic configuration of the HL-2A tokamak. Our results indicate that the deeper injection depth can be obtained with a supersonic molecular beam (SMB) with smaller density and larger width. However, the injection depth decreases when the beam density or the beam width increases. The residence time of the beam front can be lengthened by increasing the beam density and widening the beam width. If the beam density increases or the beam width enlarges, not only the injection depth decreases, but also the residence time shortens. The front of the atom density exhibits the behaviors analogous to that of the SMB, namely, both its depth and its residence time decreases with beam density increasing and beam width decreasing. At the same time, the dissociation rate has a larger range in the spatiotemporal coordinate. The global growth of dissociation rate is inhibited by the molecular dissociation localization. However, the localization of the molecular dissociation accelerates the local growth of the dissociation rate, and the global growth of the molecular dissociation rate is promoted. When the promoting effect is dominant, under the condition of constant flux and fixed injection speed, the smaller molecular injection width will lead to the shallower molecular penetration depth. The simulation results suggest that if we attempt to promote the fueling efficiency and to increase the injection depth of SMBI, we should utilize the SMBI with a smaller density and larger beam width. Of course, the concrete influences of the SMBI on injection depth and fueling efficiency should be studied further by varying other relevant parameters of the SMB and the backgroud plasma.