Reliable and accurate analysis of local stresses in structural problems of fiber-reinforced laminated composites involving nonuniform geometry is of utmost practical importance, especially when they are subjected to local loads and supports. In this research, a new study of ply stresses in a partially guided, nonuniform, short composite column of hybrid laminates, subjected to an eccentrically distributed loading is conducted using an efficient computational scheme. The analytical modeling of the present mixed-boundary-value problem of laminated structure is realized in terms of a single scalar function of space variables (called as displacement-potential function), which is defined by the displacement components of plane elasticity, and is governed by a single fourth-order partial-differential equation of equilibrium. In this modeling approach, the original three-dimensional symmetric laminated column is reduced to a plane-stress scalar-field problem of an equivalent imaginary lamina in an attempt to obtain the corresponding strain field (global laminate strain), which is then used to determine the stress fields of individual plies through the respective transformed reduced stiffness matrices. A finite-difference based computational scheme is developed to solve the representative nonuniform equivalent lamina in terms of the displacement-potential function, which is however well capable of dealing with different ply materials as well as fiber orientations, together with the associated mixed and changeable physical conditions along the boundaries of the column. A 28-ply balanced hybrid laminate composed of boron-epoxy and glass-epoxy plies with various fiber orientation is considered as the structural material for the present column. The stress fields obtained for individual plies as well as the overall laminate are analyzed in the perspective of a number of practical issues of structural design, which include material hybridization, eccentricity of loading and attachment of partial guides to the column. The design stresses of the nonuniform laminated column are identified to be affected significantly by the material and orientation of fibers as well as the laminate hybridization. An attempt is also made to verify the soundness and accuracy of the present computational scheme through the comparison of the present potential-function solutions with those obtained by the conventional computational method.