The harmonic in distribution systems becomes an important problem due to an increase in nonlinear loads. This paper presents a new approach based on a graph algorithm for optimum placement of passive harmonic filters in a multi-bus system, which suffers from harmonic current sources. The objective of this paper is to minimize the network loss, the cost of the filter and the total harmonic distortion of voltage, and also enhances voltage profile at each bus effectively. Four types of sub-graph have been used for search space of optimization. The method handles standard capacitor sizes in planning filters and associated costs. In this paper, objective function is not differential but eases solving process. The IEEE 30 bus test system is used for the placement of passive filter. The simulation has been done to show applicability of the proposed method. Simulation results prove that the method is effective and suitable for the passive filter planning in a power system.