The pursuit of quantum spin liquid (QSL) in the Kitaev honeycomb magnets has drawn intensive attention recently. In particular, α-RuCl3 has been widely recognized as a promising candidate for the Kitaev QSL. Although the compound exhibits an antiferromagnetic order under zero field, it is believed to be endowed with fractionalized excitations and can be driven to the QSL phase by magnetic fields. Here, based on a realistic K−J−Γ−Γ′ model for α−RuCl3 we exploit the exponential tensor renormalization group approach to explore the phase diagram of the compound under magnetic fields. We calculate the thermodynamic quantities, including the specific heat, Gruneisen parameter, magnetic torque, magnetotropic susceptibility, and so on, under a magnetic field with a tilting angle θ to the c∗-axis perpendicular to the honeycomb plane. We find an extended QSL in the angle-field phase diagram determined with thermodynamic responses. The gapless nature of such field-induced QSL is identified from the specific heat and entropy data computed down to very low temperatures. The present study provides guidance for future high-field experiments for the QSL in α−RuCl3 and other candidate Kitaev magnets.