We present a map of the three-dimensional (3D) distribution of dust in the Orion complex. Orion is the closest site of high-mass star formation, making it an excellent laboratory for studying the interstellar medium and star formation. We used data from the Gaia-TGAS catalogue combined with photometry from 2MASS and WISE to get the distances and extinctions of individual stars in the vicinity of the Orion complex. We use a Gaussian process and adopt a non-parametric method to infer the probability distribution function of the dust densities at arbitrary points throughout the region. We map the dust distribution towards different parts of the Orion complex. We find that the distance and depth of the cloud are compatible with other recent works, which show that the method can be applicable to local molecular clouds to map their 3D dust distribution. We also demonstrate the danger of only using colours of stars to derive their extinctions without considering further physical constraints, such as the colour-magnitude diagram (CMD).