© 2022 The Physical Society of the Republic of China (Taiwan)The outcome of the bimodal random magnetic field acting up or down along the z-axis on the spins of spin-1 with equal probability is investigated by using the lowest approximation of the cluster-variation method in the Blume–Capel model. The equal probability, [Formula presented], causes the model to give phase transitions of the form either second- or first-order. The phase diagrams of the model are computed on the (D,kBT/J) and (h,kBT/J) planes by taking into account the thermal variations of the order-parameters. The obtained phase diagrams reveal different phase regions with ground state values of 1 and 1/2 in addition to tricritical and critical end points. Simple and double hysteresis loops are also observed in the model.