  In this paper, we study the family ${\mathcal C}_{H}^0$ of sense-preserving
complex-valued harmonic functions $f$ that are normalized close-to-convex
functions on the open unit disk $\mathbb{D}$ with $f_{\bar{z}}(0)=0$. We derive
a sufficient condition for $f$ to belong to the class $\CC_{H}^0$. We take the
analytic part of $f$ to be $zF(a,b;c;z)$ or $zF(a,b;c;z^2)$ and for a suitable
choice of co-analytic part of $f$, the second complex dilatation
$w(z)=\bar{f_{\bar{z}}}/f_z$ turns out to be a square of an analytic function.
Hence $f$ is lifted to a minimal surface expressed by an isothermal parameter.
Explicit representation for classes of minimal surfaces are given. Graphs
generated by using Mathematica are used for illustration.
