This paper proposes a novel evolution strategy for noisy function optimization. We consider minimization of the expectation of a continuous domain function with stochastic parameters. The proposed method is an extended variant of distance-weighted exponential evolution strategy (DX-NES), which is a state-of-the-art algorithm for deterministic function optimization. We name it DX-NES for uncertain environments (DX-NES-UE). DX-NES-UE estimates the objective function by a quadratic surrogate function. In order to make a balance between speed and accuracy, DX-NES-UE uses surrogate function values when the noise is strong; otherwise it uses observed objective function values. We conduct numerical experiments on 20-dimensional benchmark problems to compare the performance of DX-NES-UE and that of uncertainty handling covariance matrix adaptation evolution strategy (UH-CMA-ES). UH-CMA-ES is one of the most promising methods for noisy function optimization. Benchmark problems include a multimodal function, ill-scaled functions and a non-C² function with additive noise and decision variable perturbation (sometime called actuator noise). The experiments show that DX-NES-UE requires about 1/100 times as many observations as UH-CMA-ES does on well-scaled functions. The performance difference is greater on ill-scaled functions.