For the first time, the angular non-critical phase-matching (A-NCPM) second-harmonic-generation (SHG) characteristics of a family of monoclinic oxoborate crystals, RECa4O(BO3)3 (RECOB, RE = Tm, Y, Gd, Sm, Nd and La), were comprehensively investigated. For all of the realizable A-NCPM SHG styles, the feature parameters including PM wavelength, angular, wavelength and temperature acceptance bandwidths, have been derived from the theory and verified by the experiments. We discovered that the closer the ion radius between RE3+ and Ca2+, the smaller the birefringence, and the better the A-NCPM SHG properties. As a result, for the Type-I SHG on Y-axis which has the largest effective nonlinear optical coefficient (deff) among the three realizable A-NCPM styles, NdCOB crystal presents the longest PM wavelength (927 nm), the largest angular acceptance bandwidth (Δθ⋅l1/2 = 84.3 mrad·cm1/2, Δϕ⋅l1/2 = 58.8 mrad·cm1/2), and the broadest wavelength acceptance bandwidth (8.7 nm). This discovery will contribute to the design of new NCPM materials, at the same time the parameter formula will be helpful for the theoretical prediction of NCPM performance.