Modular multilevel converters (MMC) have proven to be a viable candidate for high-voltage direct current transmission systems. Here, asymmetric modular multilevel converters (A-MMC) are introduced wherein each series connected module has two half-bridge (HB) submodules, with asymmetric voltage rating. Compared to conventional symmetric MMCs, such systems offer the following benefits: (i) generation of four distinct voltage levels using one module; (ii) 33% lesser semiconductor and gate drive requirement; (iii) higher system efficiency; (iv) reduction in overall cost and size. A hybrid pulsewidth modulation technique generates optimised switching pulses of the A-MMC. A novel voltage balancing algorithm is proposed to stabilise each asymmetric HB submodule at the rated voltage. Circulating current control is implemented to suppress the dominant second harmonic in the arm currents of the A-MMC. Detailed simulations in MATLAB/Simulink are performed to validate the operation and control. A quantitative and qualitative comparison with conventional MMCs is also presented in terms of the converter losses, output voltage/current total harmonic distortion, capacitor ripple voltages, circulating currents etc.