In the context of the development of the new era, computer network technology has become an indispensable and important technological means in people’s daily work and life. Through network technology, information resources can be collected, integrated, processed, and applied, thereby improving information analysis and mining capabilities, constructing big data environments for various industries, providing convenient and fast intelligent information services, and promoting social transformation and development. However, in practical development, network security issues seriously affect information security and social stability, and computer viruses and hackers pose a huge threat to computer systems. The computer network security evaluation is the MAGDM problems. Recently, the Logarithmic TODIM (LogTODIM) and TOPSIS technique has been utilized to cope with MAGDM issues. The interval neutrosophic sets (INSs) are utilized as a technique for characterizing uncertain information during the computer network security evaluation. In this paper, the interval neutrosophic number Logarithmic TODIM-TOPSIS (INN-LogTODIM-TOPSIS) technique is conducted to solve the MAGDM under INSs. Finally, a numerical case study for computer network security evaluation is utilized to validate the proposed technique. The prime contributions of this paper are put forward: (1) The entropy technique based on score values and accuracy value are conducted to obtain weight information under INSs; (2) an integrated INN-LogTODIM-TOPSIS technique is conducted to put forward the MAGDM issue; (3) An illustrative example for computer network security evaluation has been accomplished to put forward the INN-LogTODIM-TOPSIS technique.