We present a general, parallelizable, load balancing algorithm for unstructured grid-based problems that belong to the so-called diffusion class and employ a give-and-take concept among neighbouring subdo-mains. The algorithm is found to converge very quickly to almost perfect load balance while minimizing the surface-to-volume ratio of the domains. The algorithm can be used for problems whose cost grows nonlinearly with the number of elements, because it measures continuously the computational cost to be incurred for each subdomain. This is an advantage over the recursive bisection algorithms currently in use, which assume a linear relationship between the computational cost and the number of elements.