Currently, most of the researches in molecular communication (MC) domain focus on the static MC scenarios. However, some envisioned important MC applications require mobile MC system. The investigation on mobile MC, especially the signal detection of mobile MC is limited. This work considers the problem of signal detection for mobile MC scenarios where the receiver nano-machine performs random movement. Due to the random movement of the receiver, the channel impulse response (CIR) changes over time which makes the received signal stochastic and complicated. This further complicates the signal detection in mobile MC and leads to that the state-of-the-art signal detection schemes for static MC scenarios fail for the mobile MC scenarios. To solve this issue, an adaptive detection scheme has been proposed by our group previously, based on dynamic estimation of the stochastically varying distance between the transmitter and receiver and the reconstruction of CIR in each interval. However, its computational complexity is high. Limited capability of current nano-machines desire low-complexity detection algorithm. In this work, we further propose an adaptive detection scheme for mobile MC with a low computational complexity by utilizing the local convex property of the CIR. With on-off keying (OOK) modulation, the signal of symbol "1" presents local convex property while that of symbol "0" presents local concave property. The convexity extent varies with the stochastic distance. A simple indicator, local maximum convexity is proposed which adapts to the stochastic distance. By comparing the adaptive indicator with an adaptive threshold within each symbol interval, the signal is detected without the need to estimate the stochastically changing distance or to reconstruct the CIR. Therefore, the computational load is effectively reduced. Numerical simulations are performed to evaluate the proposed scheme. The results show that the proposed scheme achieves good detection accuracy with low computational complexity and it could be a promising detection scheme for mobile MC scenarios.