We report an experimental investigation of a laser-gas-converter approach for generating high-yield ultrashort MeV positrons. We observe that MeV electrons with a high charge of several tens of nC can be well generated by a , laser interacting with a high-density gas jet. However, it is shown that the propagation of the highly charged electron beam is significantly inhibited because the electrons are reflected by the sheath potential in the density decreasing region of the gas target, thus leading to a low positron yield. Consequently, by using an integrated nozzle-converter design to eliminate the density falling ramp of the gas target such that the electron refluxing is inhibited, we observe a significant enhancement of positron yield (up to a factor of 15), finally reaching a positron yield of . This high-yield ultrashort MeV positron may have great potential toward the simulation of astrophysical pair plasma.