We propose a new class of finite-state vector quantizers (FSVQs), called gradient match vector quantizers (GMVQs), in the image coding framework. GMVQs can be considered more general than previously proposed side match vector quantizers (SMVQs) since more border pixels between two neighboring blocks are considered in the state codebook design. Moreover, the concept of gradient matching used in GMVQs can be adjoined to another previously proposed overlap match vector quantizers (OMVQs). Thus another new class of FSVQs are proposed and named as gradient and overlap match vector quantizers (GOMVQs). GMVQs and GOMVQs utilize the 2-D spatial continuity of the pixel gradient as well as the high spatial correlation of pixels in typical grayscale images. Both minimize the gradient errors of the border pixels between blocks in ordinary vector quantization of images. In addition to reducing the granular noise that causes the annoying effect of visible pixel block boundaries, the proposed GMVQs and GOMVQs also can preserve the global gradient among the block boundaries and reduces more step noise than SMVQs and OMVQs in the area of high contrast edges. Experiments with the ‘‘Lena’’ image show that the proposed GMVQ can achieve the performance superior to those of SMVQ maximum more than 1 dB peak signal-to-noise ratio (PSNR) under the same bit rate. On the other hand, GOMVQs can achieve further bit rate reduction (about 0.14 to 0.3 bit/pixel) than OMVQ using the variable length noiseless code for the channel symbols.