Recent studies on Rb2Ti2O5 crystals have demonstrated remarkable electrical properties. This material exhibits colossal electrical polarization between 200 K and 330 K. In the present work, we report on the observation of memory effects in Rb2Ti2O5 due to charge accumulation and we discuss the genuine memristive character of this material. An analytical model is proposed for the system, which takes into account the ionic diffusion and ionic migration and is in good agreement with the observed volatile memristive properties of the material.