Circular dichroism (CD) and asymmetric transmission (AT) are important in the field of negative refractive index media and perfect polarization converters. A large difference between T++ and T-- in the transmission matrix T leads to a large CD effect, whereas a large difference between T-+ and T+- leads to a large AT effect. To achieve large CD and AT effects simultaneously, we theoretically analyzed the transmission matrix T and proposed the chiral plasmonic nanostructure of twist nanoslit-nanorod arrays (TNNAs) in this study. Results calculated by the finite element method show that, at around resonant wavelengths, the spectra of T++ and T-- correspondingly present peaks and valleys leading to a large CD effect. Meanwhile one of the spectra for T-+ and T+- presents valleys and another presents peaks leading to a large AT effect. More importantly, the magnitude of CD is equivalent to that of AT. In addition, the CD and AT effects strongly depend on the geometric parameters of TNNAs. Overall, these results are useful for designing chiral plasmonic nanostructures with large CD and AT effects.