Cities, retailers, and delivery services are trying to find more environmental friendly solutions for last mile delivery. One very promising and partly used option are cargo bicycles. A critical factor of cargo bicycles is their travel speed, which depends on the mass of the load and the gradient of the chosen streets. Therefore, we define load-dependent travel speed and introduce the vehicle routing problem with load-dependent travel times (VRPLTT). We introduce a mixed-integer programming formulation and show the benefits of considering load-dependent travel times in last mile delivery with cargo bicycles. To efficiently solve larger instances, we develop an adaptive large neighborhood search (ALNS). For the numerical study, we introduce a new set of instances and show that the travel time can be reduced by 4.5% on average and up to 22% compared to the vehicle routing problem with time windows. Moreover, ignoring the load-dependent travel times can lead to the underestimation of travel time in such a way that time windows are violated.