We investigate the misspecified linear contextual bandit (MLCB) problem, which is a generalization of the linear contextual bandit (LCB) problem. The MLCB problem is a decision-making problem in which a learner observes $d$-dimensional feature vectors, called arms, chooses an arm from them, and then obtains a reward of the chosen arm in each round. The learner aims to maximize the sum of the rewards over $T$ rounds. In contrast to the LCB problem, the rewards in the MLCB problem may not be represented by a linear function in feature vectors, but is approximated by a linear function with additive approximation parameter $\varepsilon \geq 0$. In this paper, we propose an algorithm that achieves regret bound $\tilde{O}(d\sqrt{T} + \eps\sqrt{d}T)$, where $\tilde{O}(\cdot)$ ignores polylogarithmic factors in $d$ and $T$. This is the first algorithm for the MLCB problem that works without knowing the approximation parameter $\varepsilon$ in advance. The obtained regret bound matches the regret bound by Lattimore et al. (2020) when $\varepsilon$ is known in advance. We remark that the proposed algorithm is optimal when $\varepsilon = 0$, i.e., for the case of the LCB problem.