Using the pseudopotential plane wave (PPPW) method, we performed first principles calculation for the multilayer relaxations and the electron properties of the high-Miller-index stepped Cu(311), (511), (331) and (221) surfaces, which are expressed by 2(100)×(111), 3(100)×(111), 3(111)×(111) and 4(111)×(111), respectively, in the terrace-step notation, i.e. n(hkl)×(uvw). The interlayer relaxations of them are -+-…, --+-…, --+-… and ---+-…, respectively, which follow the atom-row trend: for stepped Cu surface which has n atom rows in the (100) or (111) terrace, the outermost n－1 interlayer spaces contract, then the n interlayer space expands, and the following n+1 interlayer space contracts again. For the stepped surfaces with the same (hkl)×(uvw), the larger the number of atom rows n in the terrace, the greater the contraction magnitude for Δd1,n. We did not find any indication of anomalous relaxation behavior for Cu(511) and (331) as mentioned in some references. Below Fermi energy level, the density of states of the first layer atom at stepped edge has the largest peak value in higher energy regions and has no peak in lower energy regions, so the first layer atom is most unstable and can be dislodged and peeled off more easily than other surface atoms. For the stepped surfaces with the same (hkl)×(uvw), the curves of the density of states have similar shapes for the atoms at the step edge, at the corner, at the terrace and near the corner, and the atoms under the step edge and near the corner.