This paper studies zeroth-order optimization for stochastic convex minimization problems. We propose a parameter-free stochastic zeroth-order method (POEM), which introduces a step-size scheme based on the distance over finite difference and an adaptive smoothing parameter. Our theoretical analysis shows that POEM achieves near-optimal stochastic zeroth-order oracle complexity. Furthermore, numerical experiments demonstrate that POEM outperforms existing zeroth-order methods in practice.