The paper is devoted to a novel explicit technique, the particle transport method (PTM), for solving linear convection problems. While being a Lagrangian (characteristic based) method, PTM has the advantage of Eulerian methods to represent the solution on a fixed mesh. The proposed approach belongs to the class of monotone high-resolution numerical schemes, possesses the property of unconditional stability and works with structured and unstructured meshes. It is also demonstrated that the method has a linear computational complexity. The performance of the presented algorithm is tested on one- and two-dimensional benchmark problems. The numerical results confirm that the method has the 2nd-order spatial accuracy and can be significantly faster than the grid-based methods of the same order. Copyright © 2006 John Wiley & Sons, Ltd.