This paper proposes a novel method for simulating a three-dimensional (3D) random field conditional on site data. It is based on the assumption of separable auto-correlation in the vertical and horizontal directions. This novel method adopts special simulation techniques so that it can handle incomplete site data (e.g., missing data at some depths). Moreover, it can simulate a 3D conditional random field in a computationally efficient way without the need to invert and store large matrices. The proposed method simulates a 3D conditional random field with two steps. The first step simulates the missing site data to make the site data complete. The second step simulates the conditional random field at locations not explored by the soundings/boreholes. A simulated example is adopted to illustrate the effectiveness of the proposed method. •A method for simulating a 3D random field conditioning on incomplete data is proposed.•The method can capture the marginal statistics and auto-correlation of the random field.•The method does not need to engage in mathematical operations of large matrices.