Iterative Closest Point (ICP) is a widely used method for performing scan-matching and registration. Being simple and robust method, it is still computationally expensive and may be challenging to use in real-time applications with limited resources on mobile platforms. In this paper we propose novel effective method for acceleration of ICP which does not require substantial modifications to the existing code.This method is based on an idea of Anderson acceleration which is an iterative procedure for finding a fixed point of contractive mapping. The latter is often faster than a standard Picard iteration, usually used in ICP implementations. We show that ICP, being a fixed point problem, can be significantly accelerated by this method enhanced by heuristics to improve overall robustness. We implement proposed approach into Point Cloud Library (PCL) and make it available online. Benchmarking on real-world data fully supports our claims.