The simulation of distributed targets is very important to the design of synthetic aperture radar （SAR） systems. Since the end product is SAR images

the echo of SAR signals needs to be simulated and then processed form SAR images

and the parameters needs to be measured and the performance of the images should be

and then evaluated. The designing parameters of SAR could be adjusted to meet the requirement of users before developing SAR systems

specially in space-borne SAR systems. The simulation data is also needed during the developing and debugging of a space-borne SAR real-time processor. Another purpose of simulation is to supply a great deal of simulation images to train image users of space-borne SAR before it launch. Since significant computation is required to simulate a large area distributed targets

it may speed a lot of time

so it is very important to research a more efficient algorithm. A fast algorithm based on FFT is presented in this paper. It reviews the procedure of SAR systems return wave formed. A distributed target can be divided into many more facets

and each facet can be considered as a point targets with specific Radar Cross-Section （RCS） and unlimited small size. Generally speaking

the SAR raw signal is the appropriate superposition of returns from each facet. Noticeable

each return from every facet is the convolution of an impulse with specific amplitude and phase and the transmitting signal of SAR. So we can calculate the superposition of each impulse from each facet first. And then we can get the Fourier Transform （FT） of returns from all facets by multiply the Fourier Transform of impulses and transmitting signal. Finally

the raw returns wave can be generated by taking an Inverse Fourier Transform （IFT）. Since SAR is a discrete and band-limited system

the impulse can be calculated by an interpolation with sinc function kernel in time-domain. And the Fourier Transform can be calculated using fast Fourier Transform （FFT）. Interpolating error depends on the amount of interpolated points and the impulse position between two sampling points. More interpolated points

less error

and impulse position is closed to any of the two sampling points

the error is decreased. The relationship between the error and the two factors is presented in detail in this paper. To improve the precision of interpolations

the amount of interpolated points can be increased. But this method may increase computation linearly. The other method is reducing the interval of sampling points. Based on the second idea

an improved algorithm is introduced. It refer to upsampling and extending spectrum before Interpolating

and a low-pass filter and downsampling after Fourier Transform. This algorithm can improve efficiency and precision as the cost increasing its FFT computation. Finally

the algorithm is implemented in a code whose performance is described and illustrated by a number of examples.