Unbalanced traffic load offered to the nodes making up a path in the network guaranteeing quality-of-service has been known as a main cause deteriorating the capability of the path in admitting traffic flows. Several path load balancing methods have been developed to resolve this problem which used a feedback control scheme that adjusts the delay budget of a flow allocated to each node according to the conditions of available resource in the path. Because of no consideration about the probabilistic characteristics of the service quality, it is impossible for them to prevent in advance a bottleneck on the path which leads to a native restriction in the improvement of the capability being deteriorated. This paper proposes a preventive intra-path load balancing method applicable to the RSVP system which is based on the probabilistic characteristics of the quality-of-service of the offered load. The results of the simulation of the proposed method on a simple evaluation network showed that it provides the gain of 4~22% compared to the legacy one in terms of the number of admitted flows.