Orthogonal arrays are widely used in manufacturing and high-tech industries for quality and productivity improvement experiments. For reasons of run size economy or flexibility, nearly orthogonal arrays are also used. The construction of orthogonal or nearly orthogonal arrays can be quite challenging. Most existing methods are complex and produce limited types of arrays. This article describes a simple and effective algorithm for constructing mixed-level orthogonal and nearly orthogonal arrays. It can construct a variety of small-run arrays with good statistical properties efficiently.