The reality TV star welcomed his first child with partner Sophie Church earlier this year and he has kept fans up-to-date ever since.
On Wednesday Jake shared an adorable video on Instagram showing Leo resting on a cushion.
The caption reads: "I can't stop staring at him.... sorry for the over posting but I'm just so in love...,' he wrote alongside the post.
"Five weeks on Friday!! Little warrior!! Also thanks for all the support over the last week! Social media can be a dark place, but it's also full of amazing people!! #dad #baby #babyboy #family #love."
Jake's post comes after he called out the cruel messages he had received about Leo's appearance, with some trolls saying he is "ugly as f*ck" and "needs botox".
The I'm a Celebrity... Get Me Out of Here star said "maybe people just shouldn't troll" in the post.
"REAL POST... So in the past week this little man has been told he needs Botox, that he's ugly as f**k and that he's weird looking, me myself have also been told stay off social media if you don't want to be trolled, it's so baffling to me that I should have to stay off social media if I don't want my four-week-old trolled.
"I don't mind people giving me s**t, as sad as it is I've had to get used to being called 'irrelevant', 'ugly', 'attention seeking', and the list goes on.
"But to troll a innocent child is so wrong and the people doing it seriously need to seek help.
"Also why should I stay off social media if I don't want him trolled the thought process of some people is shocking, maybe people just shouldn't troll?
"I enjoy social media it's full of lovely people who are supportive and I like sharing my ups and downs, I try and be real as possible, but unfortunately there is a dark side of social media and something needs doing about it.
"Anyway rant over! The lion is four weeks today! Cute af! Love you son @leooliverq."
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