A method of traffic engineering (TE) based on the method of multi-path routing is proposed in the study. Today, one of the main challenges in networking is to organize an efficient TE system that will provide such parameters of quality of service (QoS) as the allowable value of packet loss and time for traffic re-routing. Traditional one-way routing facilities do not provide the required quality of service (QoS) parameters for TE. Modern computer networks use static and dynamic routing algorithms, which are characterized by big time complexity and a large amount of service information. This negatively affects the overall state of the network, namely: leads to network congestion, device failure, loss of information during routing and increases the time for traffic re-routing. Research has shown that the most promising way to solve the TE problem in computer networks is a comprehensive approach, which consists of multi-path routing, SDN technology and monitoring of the overall situation of the network. This paper proposes a method of traffic engineering in a software-defined network with specified quality of service parameters, which has reduced the time of traffic re-routing and the percentage of packet loss due to the combination of the centralized TE method and multi-path routing. From a practical point of view, the obtained method, will improve the quality of service in computer networks in comparison with the known method of traffic construction.