In computed tomography (CT), the polychromatic characteristics of x-ray photons emitting from source and absorbed by detector lead to beam-hardening effects in signal detection and image formation, especially in situations where a highly attenuating object (e.g., bone or metal in-plant) is in x-ray beam. Usually, the method called bone bam-hardening correction is employed to suppress the beam-hardening effects, in which either a scaling factor or a vector needs to be pre-determined via tedious physical experiments. Based on the Helgasson-Ludwig consistency condition (HLCC), a data consistency condition based beam-hardening correction has been proposed to avoid such a tedious parameter determination. However, the HLCC requires the involvement of neighboring projection views acquired at a relatively uniform and sufficient sampling rate, which hinders its application in the case wherein the sampling in view is sparse. Having recognized the flexibility of data integral invariant (DII), we extend the HLCC-based method by proposing a DII based objective function in this work. Using computer-simulated projection data, we carry out a simulation study to demonstrate that the process of parameter optimization and performance of the proposed beam-hardening correction method.