The polycrystals of S = 1/2 spin-dimer compound BaCu(SeO3)2 have been synthesized by using solid-state reaction. Without long-range order, the magnetic susceptibility χ(T) curve presents two anomalies at T1 = 5K and TG = 58K due to antiferromagnetic (AFM) short-range order and short-range ferromagnetic (FM) correlations, respectively, which is further supported by the specific heat and electron spin resonance data. The high-temperature χ(T) curve follows the Curie-Weiss law with θCW = 11.3K, showing the dominant intradimer FM interaction. The magnetization M(H) curve at 2K is characteristic of an AFM-FM transition at 0.4T, suggesting the weak interdimer AFM couplings. The density function theory calculations and quantum Monte Carlo simulations allow an estimation of the intradimer and interdimer exchanges with J1/kB = 39.09K, J2/kB = −1.51K, and J3/kB = −1.68K. Interestingly, the χ−1(T) curve within θCW <T <TG deviates downward from paramagnetic Curie-Weiss behavior, mimicking the Griffiths-like phase. This is further supported by the ac magnetic susceptibility and magnetic relaxation measurements. The competing intradimer FM and interdimer AFM exchanges with a subtle ratio between them are proposed to be responsible for the formation of Griffiths-like phase.