Let h = u + iv, where u, v are real harmonic functions in the unit disc A. Such functions are called complex mappings harmonic in A. The function h may be written in the form h = f + g, where f,g are functions holomorphic in the unit disc, of course. Studies of complex harmonic functions were initiated in 1984 by J. Clunie and T. Sheil-Small () and were continued by many others mathematicians. We can find some papers on functions harmonic in A, satisfying certain coefficient conditions, e.g. , , , , . We investigate some more general problem, i. e. a coefficient inequality with any fixed sequence of real positive numbers.