In this paper, we propose new low-hardware-cost motion estimation with a large search range for VLSI multimedia processors. It reduces the hardware amount required for pixel comparison by reducing both the spatial-resolution and bit-resolution of pixel values. Low-hardware-cost block-matching criterion is also employed. To avoid performance degradation from low resolution, we introduce an "outlier" pixel with large overload quantization error in the search window, and a search position is excluded from the motion estimation if its corresponding search window block contains one or more outliers. The proposed motion estimation is easy to implement in VLSI multimedia processors, and it significantly reduces the hardware amount when the search range is larger than 6464. In MPEG2 MP@ML video compression with 128128 search range, it reduces the hardware cost to 1/144 that of the full search algorithm, while its degradation of peak signal-to-noise ratio is 0.32 dB.