In this paper, a model of PI-speed control current-driven induction motor based on indirect field oriented control (IFOC) is addressed. To assess the complex dynamics of a system, different dynamical properties, such as stability of equilibrium points, bifurcation diagrams, Lyapunov exponents spectrum, and phase portraits are characterized. It is found that the induction motor model exhibits chaotic behaviors when its parameters fall into a certain region. Small variations of PI parameters and load torque affect the dynamics and stability of this electric machine. A chaotic attractor has been observed and the speed of the motor oscillates chaotically. Numerical simulation results are validating the theoretical analysis.