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In this paper, we consider the unconstrained optimization problem under the following situation: (S1) The objective function is evaluated with a certain amount of error, (S2) the error is controllable, that is, the objective function can be evaluated in any desirable accuracy, and (S3) the evaluation with higher accuracy requires more computation time. This situation arises in many fields such as engineering and financial problems, where the objective function value results from a huge amount of numerical calculation or simulation. Under (S1)—(S3), algorithms using derivatives of the objective function are not applicable. To date, there exist several algorithms which use the objective function values only. Conn et al. proposed the Derivative-Free Optimization method (DFO) as such an algorithm. The DFO generates a sequence of minimizers of quadratic model functions derived from sample points and their objective function values. Moreover, it adopts a trust-region framework for global convergence. Conn et al. shows its global convergence when the objective values at sample points are evaluated accurately. To apply DFO for the problem under (S1) and (S2), the objective function should be calculated with high accuracy in the whole step of DFO. However, computations with high accuracy require a large amount o