Quantized conductance is observed at zero magnetic field and room temperature in metal-insulator-metal structures with graphene submicron-sized nanoplatelets embedded in a 3-hexylthiophene (P3HT) polymer layer. In devices with medium concentration of graphene platelets, integer multiples of G₀ = 2e²/h = 12.91 (kΩ)⁻¹, and in some devices partially quantized including a series of with (n/7) × G₀, steps are observed. Such an organic memory device exhibits reliable memory operation with an on/off ratio of more than 10. We attribute the quantized conductance to the existence of a 1-D electron waveguide along the conductive path. The partial quantized conductance results likely from imperfect transmission coefficient due to impedance mismatch of the first waveguide modes.