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We study a two-band dispersive Sachdev-Ye-Kitaev (SYK) model in 1+1 dimension. We suggest a model that describes a semimetal with quadratic dispersion at half filling. We compute the Green's function at the saddle point using a combination of analytical and numerical methods. Employing a scaling symmetry of the Schwinger-Dyson equations that becomes transparent in the strongly dispersive limit, we show that the exact solution of the problem yields a distinct type of non-Fermi liquid with sublinear ρ∝T^{2/5} temperature dependence of the resistivity. A scaling analysis indicates that this state corresponds to the fixed point of the dispersive SYK model for a quadratic band touching semimetal.