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For past few decades, magnetic resonance imaging (MRI) has been increasingly used for a wide variety of clinical and biological research due to its excellent contrast of soft tissues in high resolution. MRI is performed in roughly two sequential procedures: excitation and acquisition. In excitation, magnetization in the target imaging volume is prepared, and in acquisition, its Fourier transform samples are measured. Conventional excitation entails transmitting a magnetic field in a radio-frequency (RF) with a single RF transmission coil. While most RF transmission excite single slices, one shortcoming of the single coil RF transmission is that it is very hard to spatially tailor the RF pulse deposition pattern in 2D or 3D because there is just one source for the RF transmission. Unfortunately, this is a significant limitation for multi-dimensional excitation, which recently gained much interest as a potential solution for problems such as inner-volume imaging, signal recovery for functional MRI, and robust fat-saturation. Recently, parallel excitation, simultaneous transmission of multiple RF pulses with multiple transmission coils, has been proposed to overcome this limitation of conventional single coil transmission. Many RF pulse design methods have been proposed, but most of them focused only on the optimization of the RF pulse waveforms, leaving the gradient waveforms unoptimized. In this thesis, we introduce a fast joint optimization scheme for RF pulse and gradient waveforms in parallel excitation to further enhance the excitation accuracy in both small and large tip-angle domains. We assumed an RF pulse sequence for slice-selective excitation, which is composed of trains of weighted slice-selective basis RF pulses interleaved by in-plane gradient blips. Our algorithm seeks to find effective RF pulse weights and the in-plane gradient blips considering an off-resonance effect. We applied our algorithm in various application domains, and demonstrated its potential advantages over previous methods through computer simulations. Our algorithm could achieve higher excitation accuracy than previous methods due to more accurate modeling for off-resonance effects. Also our method could provide faster computation than conventional methods performing a convex optimization or an exhaustive greedy search by performing a fast greedy search in a much reduced candidate set.