cis-Polyisoprene (PI) has type-A dipoles parallel along the chain backbone so that its large-scale (global) motion over the end-to-end distance activates slow dielectric relaxation. This relaxation was examined for entangled solutions of linear and star-branched PI under steady shear and large-amplitude oscillatory strain. For linear PI, the dielectric relaxation (detecting the end-to-end fluctuation in the shear gradient direction) was hardly affected by the steady shear in a range of Weissenberg number examined, Wi = γ̇τG < 7 with γ̇ and τG being the shear rate and the terminal relaxation time in the linear regime, whereas the viscosity η exhibited considerable thinning at those γ̇. In contrast, for star PI, the dielectric relaxation was moderately accelerated by the steady shear in a similar range of Wi but this acceleration was considerably less significant compared to the thinning of η. These rheo-dielectric features, noted also in a previous study, emerged under uniform shear without shear-banding and/or secondary flow, as confirmed in this study from particle tracking velocimetry. Thus, the rheo-dielectric difference between the linear and star PI suggests an essential difference of the entanglement dynamics of linear and star chains (without disturbance from the flow instability), which possibly reflects, at least partly, the constraint release effect at equilibrium being saturated for linear chains but not for star chains. The rheo-dielectric behavior of the linear and star PI chains was also examined under uniform, large amplitude oscillatory strain (LAOS). The relaxational current Irelax under rectangular electric field exhibited oscillatory decay with the main oscillation period being close to π/Ω (Ω = LAOS angular frequency). This behavior lent support to the previous analysis based on the Green–Kubo theorem (Uneyama et al. J. Polym. Sci. Part B: Polym. Phys. 2009, 47, 1039). The decay of the nonoscillating part of Irelax appeared to be rather insensitive to LAOS, which was in harmony with the behavior observed under steady shear.