We have designed and built GRAPE-1 (GRAvity PipE 1), a special-purpose computer for astrophysical N-body calculations. It is designed as a back-end processor that calculates the gravitational interaction between particles. All other calculations are performed on a host computer connected to GRAPE-1. For large-N calculations (N{greater-than or approximate}104), GRAPE-1 achieves about 100 Mflops-equivalent in one board of size about 40 by 30 cm at the power of 2.5 watt. The pipelined architecture of the GRAPE-1 which is specialized and optimized for the N-body calculation is the key to the high performance. The design and construction of the GRAPE-1 system are discussed. © 1990.