This study considers unsteady non-uniform open channel flow in a closed conduit with horseshoe cross-section. Effects of the flow depth, channel radius,slope of the channel, manning constant and lateral inflow on the flow velocity as well as the depth at which flow velocity is maximum were investigated. The finite difference approximation method was used to solve the governing equations because of its accuracy, stability and convergence followed by a graphical presentation of the results. The results indicated that for a given flow area, the velocity of flow increases with increasing depth and increase in the slope of the channel leads to an increase in flow velocity whereas increase in manning constant, radius of the channel and lateral inflow leads to a decrease in flow velocity. The results of this study agree with earlier researches done on related work of different open channel cross section. For example , Kwanza et al (2007) analyzed effects of channel width and slope for both trapezoidal and rectangular channels and concluded that discharges for both channels increases as the specified parameters are varied upwards. In addition, Kinyajui et al.,(2012) studied modeling of open channel flows in a circular cross section and they established that increase in cross section area, roughness coefficient, flow depth and radius of the channel leads to decrease in flow velocity. The practical applications of this study include controlling floods,irrigation and in construction of channels such as house gutters.