The invention discloses a fiber foamed concrete and a preparation method thereof. The fiber foamed concrete comprises the following raw materials in parts by weight: 5290 parts of cement, 4965 parts of water, 1.361 part of foaming solution, 1.2964 part of fly ash and 10 parts of fiber. The preparation method comprises the following steps: proportionally weighing the components; sequentially adding the cement and fly ash into a stirrer, proportionally weighing the water, uniformly stirring the mixture by the stirrer, and adding the fiber; preparing and adding the foaming solution; gradually adding the foam into the mixture, and continuously stirring until all the components are uniformly mixed; pouring the mixture into a mold on which lubricating oil is brushed, and curing in a curing chamber; after 24 hours, removing the mold; and respectively curing for 3 days, 7 days and 28 days for experimental detection. The fiber foamed concrete has the advantages of favorable thermal insulation property, favorable compression resistance and favorable bending resistance, and is applicable to a railway bed strengthening layer.