This paper presents a quadruple-band indoor base station antenna for 2G/3G/4G/5G mobile communications, which covers multiple frequency bands of 0.8-0.96 GHz, 1.7-2.7 GHz, 3.3-3.8 GHz and 4.8-5.8 GHz and has a compact size with its overall dimensions of 204× 175×39 mm3. The lower frequency bands over 0.8-0.96 GHz and 1.7-2.7 GHz are achieved through the combination of an asymmetrical dipole antenna and parasitic patches. A stepped-impedance feeding structure is used to improve the impedance matching of the dipole antenna over these two frequency bands. Meanwhile, the feeding structure also introduces an extra resonant frequency band of 3.3-3.8 GHz. By adding an additional small T-shaped patch, the higher resonant frequency band at 5 GHz is obtained. The parallel surrogate model-assisted hybrid differential evolution for antenna optimization (PSADEA) is employed to optimize the overall quadruple-band performance. We have fabricated and tested the final optimized antenna whose average gain is about 5.4 dBi at 0.8-0.96 GHz, 8.1 dBi at 1.7-2.7 GHz, 8.5 dBi at 3.3-3.8 GHz and 8.1 dBi at 4.8-5.0 GHz respectively. The proposed antenna has high efficiency and is of low cost and low profile, which makes it an excellent candidate for 2G/3G/4G/5G base station antenna systems.