Structural phase transitions of calcium strontium sulfoaluminate series, (Ca1-xSrx)8[AlO2]12(SO4)2 ((CS)AS-x) with x = 0.80-1.00, are systematically investigated by powder X-ray diffraction, dielectric measurements, and pyroelectric measurements, to clarify a phase diagram of (CS)AS-x (x = 0.80-1.00). A pure strontium sulfoaluminate, (CS)AS-1.00, is found to undergo three phase transitions, which take place successively on cooling from a prototypical cubic phase with the symmetry of Im3̅m. Though the room-temperature phase of (CS)AS-1.00 was previously reported to be of polar Pcc2, the pyroelectric measurements clarified a nonpolar character of the crystal symmetry. The dielectric measurements suggest a possibility of an antiferroelectric ground state of (CS)AS-x in the Sr-rich compositions. As x decreases, the ground state changes to a short-range-ordered state, implying a unique phase transition from the antiferroelectric state to the antiferroelectric-relaxor state. The present study provides an intriguing playground for designing new ferro/antiferroelectric materials.