Coefficient conditions for harmonic close-to-convex functions

New sufficient conditions, concerned with the coefficients of harmonic functions $f(z)=h(z)+\overline{g(z)}$ in the open unit disk $\mathbb{U}$ normalized by $f(0)=h(0)=h^{\mathrm{\prime }}(0)-1=0$, for $f(z)$ to be harmonic close-to-convex functions are discussed. Furthermore, several illustrative examples and the image domains of harmonic close-to-convex functions satisfying the obtained conditions are enumerated.