With the use of the "two-fluid model," we discuss anomalous diffusion induced by active force dipoles in viscoelastic media. Active force dipoles, such as proteins and bacteria, generate nonthermal fluctuating flows that lead to a substantial increment of the diffusion. Using the partial Green's function of the two-fluid model, we first obtain passive (thermal) two-point correlation functions such as the displacement cross-correlation function between the two-point particles separated by a finite distance. We then calculate active (nonthermal) one-point and two-point correlation functions due to active force dipoles. The time correlation of a force dipole is assumed to decay exponentially with a characteristic time scale. We show that the active component of the displacement cross-correlation function exhibits various crossovers from super-diffusive to subdiffusive behaviors depending on the characteristic time scales and the particle separation. Our theoretical results are intimately related to the microrheology technique to detect fluctuations in nonequilibrium environment.