Nonlocal correlations observed from entangled quantum particles imply the existence of intrinsic randomness.Normally,locally projective measurements performed on a two-qubit entangled state can only certify one-bit randomness at most,while non-projective measurement can certify more randomness with the same quantum resources.In this Letter,we carry out an experimental investigation on quantum randomness certification through a symmetric informationally complete positive operator-valued measurement,which in principle can certify the maximum randomness through an entangled qubit.We observe the quantum nonlocal correlations that are close to the theoretical values.In the future,this work can provide a valuable reference for the research on the limit of randomness certification.