With the construction and improvement of 5G infrastructure, more devices choose to access the Internet to achieve some functions. People are paying more attention to information security in the use of network devices. This makes lightweight block ciphers become a hotspot. A lightweight block cipher with superior performance can ensure the security of information while reducing the consumption of device resources. Traditional optimization tools, such as brute force or random search, are often used to solve the design of Symmetric-Key primitives. The metaheuristic algorithm was first used to solve the design of Symmetric-Key primitives of SKINNY. The genetic algorithm and the simulated annealing algorithm are used to increase the number of active S-boxes in SKINNY, thus improving the security of SKINNY. Based on this, to improve search efficiency and optimize search results, we design a novel metaheuristic algorithm, named particle swarm-like normal optimization algorithm (PSNO) to design the Symmetric-Key primitives of SKINNY. With our algorithm, one or better algorithm components can be obtained more quickly. The results in the experiments show that our search results are better than those of the genetic algorithm and the simulated annealing algorithm. The search efficiency is significantly improved. The algorithm we proposed can be generalized to the design of Symmetric-Key primitives of other lightweight block ciphers with clear evaluation indicators, where the corresponding indicators can be used as the objective functions.