Phase unwrapping aims to reconstruct the absolute phase from its values mod 2π, which is a key problem in many non-contact optical metrologies and is still a challenging issue in the presence of noise. We present a robust phase unwrapping method with two steps based on local denoising and the accumulation of residual map (ARM). In the first step, based on the local polynomial approximations and intersection of confidence intervals, we adopt a sine–cosine filtering and iteration algorithm to denoise the wrapped phase, which uses the periodicity of the trigonometric function to avoid the influence of phase jumps effectively. In the second step, the denoised wrapped phase is unwrapped by the improved ARMs method, in which we modify the edge regular term to avoid over-fitting and maintain edge information. The algorithm is tested with a set of numerical simulations under various noise levels, and the experimental results confirm its effectiveness and robustness.