The gravity forward modeling algorithm is a compute-intensive method and is widely used in scientific computing, particularly in geophysics, to predict the impact of subsurface structures on surface gravity fields. Traditional implementations rely on CPUs, where performance gains are mainly achieved through algorithmic optimization. With the rise of domain-specific architectures, FPGA offers a promising platform for acceleration, but faces challenges such as limited programmability and the high cost of nonlinear function implementation. This work proposes an FPGA-based co-processor to accelerate gravity forward modeling. A RISC-V core is integrated with a custom instruction set targeting key computation steps. Tasks are dynamically scheduled and executed on eight fully pipeline processing units, achieving high parallelism while retaining programmability. To address nonlinear operations, we introduce a piecewise linear approximation method optimized via stochastic gradient descent (SGD), significantly reducing resource usage and latency. The design is implemented on the AMD UltraScale+ ZCU102 FPGA (Advanced Micro Devices, Inc. (AMD), Santa Clara, CA, USA) and evaluated across several forward modeling scenarios. At 250 MHz, the system achieves up to 179× speedup over an Intel Xeon 5218R CPU (Intel Corporation, Santa Clara, CA, USA) and improves energy efficiency by 2040×. To the best of our knowledge, this is the first FPGA-based gravity forward modeling accelerate design.