In this note, the following question, not discussed well in the literature, is considered: $$\text{Is the convex hull of }A\text{ closed if }A\text{ is a closed cone in }{R}^n?$$ When $n=1$ or $2$, the answer to the above problem is affirmative. The main purpose of this brief note is to give a simple example showing that the answer is negative when $n\ge 3$.