To search for new candidates of the true and simultaneous two-proton(2p)radioactivity,the 2p decay energies(Q2p)are extracted by the Weizsacker-Skyrme-4(WS4)model,the finite-range droplet model(FRDM),the Koura-Tachibana-Uno-Yamada(KTUY)model and the Hartree-Fock-Bogoliubov mean-field model with the BSk29 Skyrme interaction(HFB29).Then,the 2p radioactivity half-lives are calculated within the generalized liquid drop model by inputting the four types of Q2p values.By the energy and half-life constraints,it is found that the probable 2p decay candidates are the nuclei beyond the proton-drip line in the region of Z≤50 based on the WS4 and KTUY mass models.For the FRDM mass model,the probable 2p decay candidates are found in the region of Z≤44.However,the 2p-decaying candidates are predicted in the region of Z≤58 by the HFB29 mass model.It means that the probable 2p decay candidates of Z＞50 are only predicted by the HFB29 mass model.Finally,the competition between the true 2p radioactivity and α-decay for the nuclei above the N=Z=50 shell closures is discussed.It is shown that 101Te,111Ba and 114Ce prefer to 2p radioactivity and the dominant decay mode of 107Xe and 116Ce is α-decay.