Gaussian-like filters are frequently used in digital signal transmission. Usually, these filters are made of lumped inductors and capacitors. In the stopband, these filters exhibit a high reflection, which can create unwanted signal interference. To prevent that, a new low-reflection ladder network is introduced that consist of resistors, inductors, and capacitors. The network models fictitious transmission lines with Gaussian-like amplitude characteristics. Starting from the analysis of this network, a procedure is developed for synthesis of a new class of lumped-element RLC filters. These filters have transmission coefficients similar to the classical Bessel filters. In contrast to the Bessel filters, the new filters exhibit a low reflection both in the stopband and passband, they have a small span of element parameters, and they are easy for manufacturing and tuning.