A diamond spin chain system, one of the one-dimensional frustrated lattices, is known to exhibit novel properties, but experimental studies have been exclusively confined to materials with a single spin component. Here, we report on the synthesis, structure, and magnetic properties of a new diamond chain compound Cu2FePO4F4(H2O)(4) 1 composed of mixed-spins of Cu2+ (S = 1/2 X 2) and Fe3+ (S = 5/2). Compound 1 crystallizes in the space group C2/c of the monoclinic crystal system with a = 7.7546(4) angstrom, b = 12.1290(6) angstrom, c = 9.9209(6) angstrom, beta = 105.29(1)degrees, and Z = 4. DC magnetization, Mossbauer spectroscopy, and heat capacity measurements revealed an antiferromagnetic order at 11.3 K with a small ferromagnetic component. It is suggested that ferrimagnetic diamond chains are arranged in an antiferromagnetic fashion (i.e., [Fe-center dot center dot center dot(up arrow)-2Cu(down arrow down arrow)-Fe(up arrow)(center dot center dot center dot)] and [Fe-center dot center dot center dot(down arrow)-2Cu(up arrow up arrow)-Fe(down arrow)(center dot center dot center dot)]) within the ab plane to cancel net magnetization, and the spin orientation of the diamond chains changes alternately along the c axis due to the magnetic anisotropy, leading to a noncollinear spin order. Furthermore, another anomaly is observed in the heat capacity at around 3 K, suggesting a successive magnetic transition or crossover due to competing magnetic interactions.