In crystalline magnets, interaction randomness is usually thought as a negative factor preventing interesting quantum phenomena to occur. However, intriguing interplay between randomness and quantumness can also leads to unique phenomena in the strongly correlated materials. Among others, the random transverse-field Ising spin chain (RTIC) hosts a renowned quantum Griffiths phase. Although the RTIC model has been regarded as a toy model for long, here we materialize this model with the compound PrTiNbO6, which has a disordered ground state with pronounced quantum fluctuations and continuous spin excitations. The observed anomalous spin dynamics of PrTiNbO6 can be accounted by the RTIC model with a consistent set of parameters determined from fitting the thermodynamic data, and it is ascribed to the quantum Griffiths rare regions in the system. Our results provide a concrete example of quantum Griffiths magnet, and offer an ideal experimental platform for investigating the dynamical properties of random many-body system.