Using value distribution theory and maximum modulus principle, we investigate the existence of the algebroid solutions of high-order algebraic differential equation, and obtain that the solution of the equation is algebraic under certain conditions. Example shows that our results are sharp. In addition, we obtain three equivalent propositions of deficiency and exceptional values in the case of algebroid solution. Example shows that our results are valuable.

algebroid function, algebraic solution, maximum modulus principle, differential equations.