For an open quantum system containing two qubits under homodyne-based feedback control, we investigate the dynamical behaviors of quantum-memory-assisted entropic uncertainty. Moreover, we analyze the influence of feedback modes and coefficients on the entropic uncertainty. Numerical investigations show that the memory qubit should be placed in a non-dissipative channel if the single dissipative channel condition can be chosen, which helps reduce the entropic uncertainty of the system. For the homodyne feedback control F =λσx (or F =λσy), due to different roles of the entangled qubits A and B, when they are subject to feedback control with different feedback coefficients λ, the exchange of feedback coefficients will cause variations of the entropic uncertainty. When the feedback coefficient corresponding to the memory qubit B is larger (λB>λA), the steady value of the entropic uncertainty will be small, which is conducive to enhancing the robustness of the system. However, for the feedback control F=λσz, the difference between the feedback coefficients has no effect on the steady values of the entropic uncertainty.