Quantum repeaters have been proposed as a way of extending the reach of quantum communication. First-generation approaches use entanglement swapping to connect entangled links along a long-distance channel. Recently, there have been proposals for first-generation quantum repeaters for continuous variables. In this paper, we present an improved continuous-variable (CV) repeater scheme using optimal Gaussian entanglement swapping. Our scheme uses the noiseless linear amplifier for entanglement distillation. We show that with the simplest configuration of the noiseless linear amplifier and under the assumption of good quantum memories and perfect sources and detectors, our scheme beats the direct transmission upper limit for shorter distances and can offer advantages over previous CV repeater schemes.