Experimental investigation of nuclear-spin effects on the electron-spin polarization in singly negatively charged InP quantum dots is reported. Pump-probe photoluminescence measurements of electron-spin relaxation in the microsecond time scale are used to estimate the time period TN of the Larmor precession of nuclear spins in the hyperfine field of electrons. We find TN to be ∼1 μs at T≈5 K, under the vanishing external magnetic field. From the time-integrated measurements of electron-spin polarization as a function of a longitudinally applied magnetic field at T≈5 K, we find that the Overhauser field appearing due to the dynamic nuclear polarization increases linearly with the excitation power, though its magnitude remains smaller than 10 mT up to the highest excitation power (50 mW) used in these experiments. The effective magnetic field of the frozen fluctuations of nuclear spins is found to be 15 mT, independent of the excitation power.