To efficiently and selectively produce 2,6-dimethyl-naphthalene by methylating naphthalene or methylnaphthalenes in the presence of a solid acid catalyst.

Naphthalene or 2-methylnaphthalene as a starting substance is allowed to react with a methylating agent, for example, methanol or dimethyl ether in the presence of a zeolite catalyst having pores with a pore size of 5.8-6.8 in the major axis where the reaction temperature is in the range of 300-450°C, the reaction pressure corresponding to the temperature attains 0.2-6.5-fold the critical pressure of the methylating agent namely under the sub-supercritical or supercritical pressure. When the density of the methylating agent is set in the range of 0.02-0.25 g/ml in the reaction system, the selectivity of 2,6-dimethylnaphthalene is increased as given in Figure 2.