In this paper, we focus on the detection of a moving point-like target embedded in uncertain signal-dependent clutter and develop robust transmit-code and receive-filter designs in slow-time. First, based on the Worst-case Signal-to-Interference-plus-Noise Ratio (W-SINR) when the second-order clutter statistics are uncertain, we establish a high-dimensional transmit-receive optimization model that considers the constant modulus constraint with non-convexity. Next, we propose an Iterative Sequential Optimization (ISO) algorithm. At each iteration, it converts a high-dimensional optimization into multiple one-dimensional fractional programming problems that can be efficiently solved using Dinkelbach’s method. Finally, we use numerical examples to confirm that the ISO can resist the uncertain knowledge of signal-dependent clutter, which enables the radar system to adapt to complicated environments. Moreover, compared to Semi-Definite Relaxation (SDR)-related and randomization methods, the proposed algorithm is superior with respect to both optimized W-SINR and computational time.