In the turbine-blade manufacturing industry, turbine-blades are machined and then are assembled to form a circular roll of blades. The roll of blades should be balanced as much as possible, since otherwise the efficiency of the turbine generator might be damaged. A locking blade is a blade whose location is fixed and a non-locking blade is a blade whose location can be freely changed. In this paper, we study methods for balancing the weights of the rotating blades for a turbine where some blades are locking blades. The turbine-blade balancing problem is formulated into a mixed-integer programming problem, which turns out to be NP-hard. A heuristic method based on the number partitioning algorithm is developed and the computational experiments show very promising results.