The present invention addresses the problem of providing a hair cosmetic composition that is provided with a first agent that contains an alkali agent and with a second agent that contains an oxidizing agent, wherein the viscosity of the first agent is high, and the first agent and second agent can be mixed by shaking. The above mentioned problem can be solved by configuring the viscosity of the first agent at 25 DEG C to be 5000-40000 mPas, configuring the viscosity of the second agent at 25 DEG C to be 100-6000 mPas, and further including the components (A)-(C) below in the second agent. (A) a higher fatty acid (B) an ampholytic surfactant (C) 0.01-5 mass% of an alkyl glycoside