In this paper, a new randomized solver (called VRDFON) for noisy unconstrained derivative-free optimization problems is discussed. Complexity results in the presence of noise for nonconvex, convex, and strongly convex functions are studied. Two effective ingredients of VRDFON are an improved derivative-free line search algorithm with many heuristic enhancements and quadratic models in adaptively determined subspaces. Numerical results show that, on the large scale unconstrained CUTEst test problems contaminated by the absolute uniform noise, VRDFON is more efficient than several state-of-the-art solvers.