Explanation
Yes, in the conventional political sense: China is a Communist Party-led state. However, this describes its governing party and political system, not the achievement of communism as the party's ultimate ideological goal.
China's Constitution identifies the country as a socialist state and establishes Communist Party leadership as a defining feature of its system. An independent Congressional Research Service analysis describes China as a Leninist party-state in which the party dominates political institutions.
Economically, the Constitution recognizes private businesses as part of a socialist market economy. The party's own constitution describes communism as an ultimate goal. Calling China communist is therefore accurate political shorthand, but it should not imply that private enterprise has been abolished or that the party claims to have completed the transition to communism.
Key takeaway
China is governed by a communist party, while its officially socialist market economy includes private enterprise.