In this study we use three-dimensional magnetohydrodynamic simulations to investigate how the dynamic state of emerging magnetic field is related to the twist of field lines. Emerging magnetic field forms a magnetic structure on the Sun where various kinds of activity such as solar flares, jets, and coronal mass ejections are observed. To understand the physical mechanism for producing such activity, we have to know the dynamic nature of this structure. Since flares are the manifestation of rapidly dissipating electric current in the corona, we also investigate the distribution of current density inside the structure and examine how it depends on the field-line twist. To demonstrate the dynamic structure of emerging magnetic field, we focus on the factors characterizing the geometric property and stratification of emerging magnetic field, such as the curvature of field line and the scale height of field strength. These two factors show that emerging field forms a two-part structure in which the central part is close to a force-free state while the outer marginal part is in a fairly dynamic state where magnetic pressure force is dominant. We discuss how the field-line twist affects the two-part structure and also explain a possible relation between electric current structure and sigmoid observed in a preflare phase.