AbstractWe study the thermodynamic properties of asymmetric quark matter and large mass quark stars within the confined-isospin-density-dependent-quark-mass model. We find that the quark matter symmetry energy should be very large in order to describe the recent discovered heavy compact stars PSR J0348+0432 ($$\text {2.01}\pm \text {0.04}M_{\odot }$$ 2.01 ± 0.04 M ⊙ ), MSP J0740+6620 ($$\text {2.14}\pm ^\text {0.10}_\text {0.09}M_{\odot }$$ 2.14 ± 0.09 0.10 M ⊙ of 68.3$$\%$$ % credibility interval and $$\text {2.14}\pm ^\text {0.20}_\text {0.18}M_{\odot }$$ 2.14 ± 0.18 0.20 M ⊙ of 95.4$$\%$$ % credibility interval) and PSR J2215+5135 (2.27$$\pm ^\text {0.10}_\text {0.09}M_{\odot }$$ ± 0.09 0.10 M ⊙ ) as QSs. The tidal deformability $$\Lambda _{1.4}$$ Λ 1.4 of the QSs is also investigated in this work, and the result indicates that $$\Lambda _{1.4}$$ Λ 1.4 may depend on the isospin effects and the strength / orientation distribution of the magnetic fields inside the quark stars.