In this paper we discuss the estimation of effort needed to update program codes according to given design specification changes. In the Object-Oriented incremental development(OOID), the requirement changes occur frequently and regularly. When a requirement change occurs, a design specification is changed accordingly. Then a program code is updated for given design specification change. In order to construct the development plan dynamically, a simple and fast estimation method of efforts forcode updating is strongly required by both developers and managers. However, existing estimation methods cannot be applied to the OOID. We therefore try to propose a straightforward approach to estimate effort for code updating, which reflects the specific properties of the OOID. We list up following factors of the effort estimation for OOID: (1) updating activities consist of creation, deletion, and modification, (2) the target to be updated has four kinds of types(void type, basic type, library type, and custom type), (3) the degree of information hiding is classified into private, protected and public, and (4) the degree of inheritance affects updating efforts. We then propose a new formula $E(P,\sigma)$ to calculate the efforts needed to update a program $P$ according to a set of design specification changes $\sigma$. The formula $E(P,\sigma)$ includes weighting parameters: $W_{upd}$, $W_{type}$, $W_{inf\mbox{-}h}$ and $W_{inht}$ according to the characteristics (1), (2), (3) and (4), respectively. Finally, we conduct experimental evaluations by applying the formula $E(P,\sigma)$ to actual project data in a certain company. The evaluation results statistically showed the validity of the proposed approach to some extent.